Elementary Algebra

Lynn Marecek

Chapter 5

Systems of Linear Equations - all with Video Answers

Educators

Section 1

Solve Systems of Equations by Graphing

Problem 1

Determine Whether an Ordered Pair is a Solution of a System of Equations. In the following exercises, determine if the following points are solutions to the given system of equations.
$$
\left\{\begin{array}{l}
2 x-6 y=0 \\
3 x-4 y=5
\end{array}\right.
$$
(a) (3,1)
(b) (-3,4)

Melissa Barry

Melissa Barry

Numerade Educator

Problem 2

Determine Whether an Ordered Pair is a Solution of a System of Equations. In the following exercises, determine if the following points are solutions to the given system of equations.
$$
\text {}\left\{\begin{array}{l}
7 x-4 y=-1 \\
-3 x-2 y=1
\end{array}\right.
$$
(a) (1,2) (b) (1,-2)

Melissa Barry

Numerade Educator

Problem 3

Determine Whether an Ordered Pair is a Solution of a System of Equations. In the following exercises, determine if the following points are solutions to the given system of equations.
$$
\left\{\begin{array}{l}
2 x+y=5 \\
x+y=1
\end{array}\right.
$$
(a) (4,-3)
(b) (2,0)

Melissa Barry

Numerade Educator

Problem 4

Determine Whether an Ordered Pair is a Solution of a System of Equations. In the following exercises, determine if the following points are solutions to the given system of equations.
$$
\left\{\begin{array}{l}
-3 x+y=8 \\
-x+2 y=-9
\end{array}\right.
$$
(a) (-5,-7)
(b) (-5,7)

Melissa Barry

Numerade Educator

Problem 5

Determine Whether an Ordered Pair is a Solution of a System of Equations. In the following exercises, determine if the following points are solutions to the given system of equations.
$$
\left\{\begin{array}{l}
x+y=2 \\
y=\frac{3}{4} x
\end{array}\right.
$$
(a) $\left(\frac{8}{7}, \frac{6}{7}\right)$ (b) $\left(1, \frac{3}{4}\right)$

Melissa Barry

Numerade Educator

Problem 6

Determine Whether an Ordered Pair is a Solution of a System of Equations. In the following exercises, determine if the following points are solutions to the given system of equations.
$$
\left\{\begin{array}{l}
x+y=1 \\
y=\frac{2}{5} x
\end{array}\right.
$$
(a) $\left(\frac{5}{7}, \frac{2}{7}\right)$ (b) (5,2)

Melissa Barry

Numerade Educator

Problem 7

Determine Whether an Ordered Pair is a Solution of a System of Equations. In the following exercises, determine if the following points are solutions to the given system of equations.
$$
\left\{\begin{array}{l}
x+5 y=10 \\
y=\frac{3}{5} x+1
\end{array}\right.
$$
(a) (-10,4) (b) $\left(\frac{5}{4}, \frac{7}{4}\right)$

Melissa Barry

Numerade Educator

Problem 8

Determine Whether an Ordered Pair is a Solution of a System of Equations. In the following exercises, determine if the following points are solutions to the given system of equations.
$$
\left\{\begin{array}{l}
x+3 y=9 \\
y=\frac{2}{3} x-2
\end{array}\right.
$$
(a) (-6,5)
(b) $\left(5, \frac{4}{3}\right)$

Melissa Barry

Numerade Educator

Problem 9

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
3 x+y=-3 \\
2 x+3 y=5
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 10

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
-x+y=2 \\
2 x+y=-4
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 11

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
-3 x+y=-1 \\
2 x+y=4
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 12

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
-2 x+3 y=-3 \\
x+y=4
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 13

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
y=x+2 \\
y=-2 x+2
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 14

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
y=x-2 \\
y=-3 x+2
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 15

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
y=\frac{3}{2} x+1 \\
y=-\frac{1}{2} x+5
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 16

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
y=\frac{2}{3} x-2 \\
y=-\frac{1}{3} x-5
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 17

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
-x+y=-3 \\
4 x+4 y=4
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 18

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
x-y=3 \\
2 x-y=4
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 19

$$
\left\{\begin{array}{l}
-3 x+y=-1 \\
2 x+y=4
\end{array}\right.
$$$$
\left\{\begin{array}{l}
-3 x+y=-1 \\
2 x+y=4
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 20

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
-3 x+y=-2 \\
4 x-2 y=6
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 21

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
x+y=5 \\
2 x-y=4
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 22

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
x-y=2 \\
2 x-y=6
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 23

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
x+y=2 \\
x-y=0
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 24

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
x+y=6 \\
x-y=-8
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 25

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
x+y=-5 \\
x-y=3
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 26

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
x+y=4 \\
x-y=0
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 27

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
x+y=-4 \\
-x+2 y=-2
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 28

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
-x+3 y=3 \\
x+3 y=3
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 29

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
-2 x+3 y=3 \\
x+3 y=12
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 30

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
2 x-y=4 \\
2 x+3 y=12
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 31

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
2 x+3 y=6 \\
y=-2
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 32

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
-2 x+y=2 \\
y=4
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 33

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
x-3 y=-3 \\
y=2
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 34

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
2 x-2 y=8 \\
y=-3
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 35

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
2 x-y=-1 \\
x=1
\end{array}\right.
$$

Satyam Gupta

Numerade Educator

Problem 36

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
x+2 y=2 \\
x=-2
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 37

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
x-3 y=-6 \\
x=-3
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 38

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
x+y=4 \\
x=1
\end{array}\right.
$$

Satyam Gupta

Numerade Educator

Problem 39

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
4 x-3 y=8 \\
8 x-6 y=14
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 40

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
x+3 y=4 \\
-2 x-6 y=3
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 41

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
-2 x+4 y=4 \\
y=\frac{1}{2} x
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 42

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
3 x+5 y=10 \\
y=-\frac{3}{5} x+1
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 43

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
x=-3 y+4 \\
2 x+6 y=8
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 44

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
4 x=3 y+7 \\
8 x-6 y=14
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 45

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
2 x+y=6 \\
-8 x-4 y=-24
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 46

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
5 x+2 y=7 \\
-10 x-4 y=-14
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 47

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
x+3 y=-6 \\
4 y=-\frac{4}{3} x-8
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 48

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
-x+2 y=-6 \\
y=-\frac{1}{2} x-1
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 49

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
-3 x+2 y=-2 \\
y=-x+4
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 50

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$$
\left\{\begin{array}{l}
-x+2 y=-2 \\
y=-x-1
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 51

Determine the Number of Solutions of a Linear System Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations.
$$
\left\{\begin{array}{l}
y=\frac{2}{3} x+1 \\
-2 x+3 y=5
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 52

Determine the Number of Solutions of a Linear System Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations.
$$
\left\{\begin{array}{l}
y=\frac{1}{3} x+2 \\
x-3 y=9
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 53

Determine the Number of Solutions of a Linear System Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations.
$$
\left\{\begin{array}{l}
y=-2 x+1 \\
4 x+2 y=8
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 54

Determine the Number of Solutions of a Linear System Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations.
$$
\left\{\begin{array}{l}
y=3 x+4 \\
9 x-3 y=18
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 55

Determine the Number of Solutions of a Linear System Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations.
$$
\left\{\begin{array}{l}
y=\frac{2}{3} x+1 \\
2 x-3 y=7
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 56

Determine the Number of Solutions of a Linear System Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations.
$$
\left\{\begin{array}{l}
3 x+4 y=12 \\
y=-3 x-1
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 57

Determine the Number of Solutions of a Linear System Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations.
$$
\left\{\begin{array}{l}
4 x+2 y=10 \\
4 x-2 y=-6
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 58

Determine the Number of Solutions of a Linear System Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations.
$$
\left\{\begin{array}{l}
5 x+3 y=4 \\
2 x-3 y=5
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 59

Determine the Number of Solutions of a Linear System Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations.
$$
\left\{\begin{array}{l}
y=-\frac{1}{2} x+5 \\
x+2 y=10
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 60

Determine the Number of Solutions of a Linear System Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations.
$$
\left\{\begin{array}{l}
y=x+1 \\
-x+y=1
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 61

Determine the Number of Solutions of a Linear System Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations.
$$
\left\{\begin{array}{l}
y=2 x+3 \\
2 x-y=-3
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 62

Determine the Number of Solutions of a Linear System Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations.
$$
\left\{\begin{array}{l}
5 x-2 y=10 \\
y=\frac{5}{2} x-5
\end{array}\right.
$$

Melissa Barry

Numerade Educator

Problem 63

Molly is making strawberry infused water. For each ounce of strawberry juice, she uses three times as many ounces of water. How many ounces of strawberry juice and how many ounces of water does she need to make 64 ounces of strawberry infused water?

Gokul R Nair

Numerade Educator

Problem 64

Jamal is making a snack mix that contains only pretzels and nuts. For every ounce of nuts, he will use 2 ounces of pretzels. How many ounces of pretzels and how many ounces of nuts does he need to make 45 ounces of snack mix?

Gokul R Nair

Numerade Educator

Problem 65

Enrique is making a party mix that contains raisins and nuts. For each ounce of nuts, he uses twice the amount of raisins. How many ounces of nuts and how many ounces of raisins does he need to make 24 ounces of party mix?

Gokul R Nair

Numerade Educator

Problem 66

Owen is making lemonade from concentrate. The number of quarts of water he needs is 4 times the number of quarts of concentrate. How many quarts of water and how many quarts of concentrate does Owen need to make 100 quarts of lemonade?

Destin Priester

Destin Priester

Numerade Educator

Problem 67

Leo is planning his spring flower garden. He wants to plant tulip and daffodil bulbs. He will plant 6 times as many daffodil bulbs as tulip bulbs. If he wants to plant 350 bulbs, how many tulip bulbs and how many daffodil bulbs should he plant?

Destin Priester

Destin Priester

Numerade Educator

Problem 68

A marketing company surveys 1,200 people. They surveyed twice as many females as males. How many males and females did they survey?

Gokul R Nair

Numerade Educator

Problem 69

In a system of linear equations, the two equations have the same slope. Describe the possible solutions to the system

Destin Priester

Destin Priester

Numerade Educator

Problem 70

In a system of linear equations, the two equations have the same intercepts. Describe the possible solutions to the system.

Destin Priester

Destin Priester

Numerade Educator