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

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)

Erika Bustos

Erika Bustos

Numerade Educator

Problem 2

In the following exercises, determine if the following points are solutions to the given system of equations.
$$
\left\{\begin{array}{l}
7 x-4 y=-1 \\
-3 x-2 y=1
\end{array}\right.
$$
(a) (b) (1,-2)

Erika Bustos

Numerade Educator

Problem 3

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)

Erika Bustos

Numerade Educator

Problem 4

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)

Erika Bustos

Numerade Educator

Problem 5

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) $\left(1, \frac{3}{4}\right)$

Erika Bustos

Numerade Educator

Problem 6

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

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

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

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

Daniel Carr

Numerade Educator

Problem 10

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

Daniel Carr

Numerade Educator

Problem 11

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

Daniel Carr

Numerade Educator

Problem 12

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

Daniel Carr

Numerade Educator

Problem 13

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

Daniel Carr

Numerade Educator

Problem 14

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

Daniel Carr

Numerade Educator

Problem 15

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

Daniel Carr

Numerade Educator

Problem 16

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

Daniel Carr

Numerade Educator

Problem 17

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

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

Daniel Carr

Numerade Educator

Problem 19

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

Daniel Carr

Numerade Educator

Problem 20

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

Daniel Carr

Numerade Educator

Problem 21

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

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

Daniel Carr

Numerade Educator

Problem 23

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

Daniel Carr

Numerade Educator

Problem 24

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

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

Daniel Carr

Numerade Educator

Problem 26

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

Daniel Carr

Numerade Educator

Problem 27

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

Daniel Carr

Numerade Educator

Problem 28

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

Daniel Carr

Numerade Educator

Problem 29

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

Daniel Carr

Numerade Educator

Problem 30

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

Daniel Carr

Numerade Educator

Problem 31

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

Daniel Carr

Numerade Educator

Problem 32

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

Daniel Carr

Numerade Educator

Problem 33

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

Daniel Carr

Numerade Educator

Problem 34

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

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

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

Daniel Carr

Numerade Educator

Problem 37

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

Daniel Carr

Numerade Educator

Problem 38

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

Daniel Carr

Numerade Educator

Problem 39

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

Daniel Carr

Numerade Educator

Problem 40

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

Daniel Carr

Numerade Educator

Problem 41

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

Daniel Carr

Numerade Educator

Problem 42

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

Daniel Carr

Numerade Educator

Problem 43

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

Daniel Carr

Numerade Educator

Problem 44

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

Daniel Carr

Numerade Educator

Problem 45

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

Daniel Carr

Numerade Educator

Problem 46

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

Daniel Carr

Numerade Educator

Problem 47

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

Daniel Carr

Numerade Educator

Problem 48

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

Daniel Carr

Numerade Educator

Problem 49

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

Daniel Carr

Numerade Educator

Problem 50

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

Daniel Carr

Numerade Educator

Problem 51

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

Erika Bustos

Numerade Educator

Problem 52

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

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

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

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

Erika Bustos

Numerade Educator

Problem 56

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

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

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

Erika Bustos

Numerade Educator

Problem 59

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

Erika Bustos

Numerade Educator

Problem 60

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

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

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

Erika Bustos

Numerade Educator

Problem 63

In the following exercises, solve.
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

In the following exercises, solve.
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

In the following exercises, solve.
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

In the following exercises, solve.
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

In the following exercises, solve.
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

In the following exercises, solve.
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 the following exercises, solve.
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 the following exercises, solve.
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