Intermediate Algebra

Lynn Marecek

Chapter 4

Systems of Linear Equations - all with Video Answers

Educators

Section 1

Solve Systems of Linear Equations with Two Variables

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.
$\left\{\begin{array}{l}-3 x+y=8 \\ -x+2 y=-9\end{array}\right.$
(a) (-5,-7)
(b) (-5,7)

Erika Bustos

Numerade Educator

Problem 3

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

Erika Bustos

Numerade Educator

Problem 4

In the following exercises, determine if the following points are solutions to the given system of equations.
$\left\{\begin{array}{l}2 x+3 y=6 \\ y=\frac{2}{3} x+2\end{array}\right.$
(a) (-6,2)
(b) (-3,4)

Erika Bustos

Numerade Educator

Problem 5

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 6

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 7

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 8

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 9

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 10

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 11

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 12

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 13

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 14

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 15

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

Daniel Carr

Numerade Educator

Problem 16

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

Daniel Carr

Numerade Educator

Problem 17

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

Daniel Carr

Numerade Educator

Problem 18

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 19

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 20

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 21

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 22

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 23

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

Willis James

Numerade Educator

Problem 24

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 25

Without graphing, 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 26

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

Erika Bustos

Numerade Educator

Problem 27

Without graphing, 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 28

Without graphing, 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 29

Without graphing, 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 30

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

MG

Melissa Grier

Numerade Educator

Problem 31

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

MG

Melissa Grier

Numerade Educator

Problem 32

In the following exercises, solve the systems of equations by substitution.
$$
\left\{\begin{array}{l}
x-2 y=-5 \\
2 x-3 y=-4
\end{array}\right.
$$

MG

Melissa Grier

Numerade Educator

Problem 33

In the following exercises, solve the systems of equations by substitution.
$$
\left\{\begin{array}{l}
x-3 y=-9 \\
2 x+5 y=4
\end{array}\right.
$$

MG

Melissa Grier

Numerade Educator

Problem 34

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

MG

Melissa Grier

Numerade Educator

Problem 35

In the following exercises, solve the systems of equations by substitution.
$$
\left\{\begin{array}{l}
-2 x+2 y=6 \\
y=-3 x+1
\end{array}\right.
$$

MG

Melissa Grier

Numerade Educator

Problem 36

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

Teresa Fuston

Numerade Educator

Problem 37

In the following exercises, solve the systems of equations by substitution.
$$
\left\{\begin{array}{l}
3 x+4 y=1 \\
y=-\frac{2}{5} x+2
\end{array}\right.
$$

Teresa Fuston

Numerade Educator

Problem 38

In the following exercises, solve the systems of equations by substitution.
$$
\left\{\begin{array}{l}
2 x+y=5 \\
x-2 y=-15
\end{array}\right.
$$

Teresa Fuston

Numerade Educator

Problem 39

In the following exercises, solve the systems of equations by substitution.
$$
\left\{\begin{array}{l}
4 x+y=10 \\
x-2 y=-20
\end{array}\right.
$$

Teresa Fuston

Numerade Educator

Problem 40

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

Teresa Fuston

Numerade Educator

Problem 41

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

Teresa Fuston

Numerade Educator

Problem 42

In the following exercises, solve the systems of equations by substitution.
$$
\left\{\begin{array}{c}
x=2 y \\
4 x-8 y=0
\end{array}\right.
$$

Teresa Fuston

Numerade Educator

Problem 43

In the following exercises, solve the systems of equations by substitution.
$$
\left\{\begin{array}{l}
2 x-16 y=8 \\
-x-8 y=-4
\end{array}\right.
$$

Erika Bustos

Numerade Educator

Problem 44

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

Teresa Fuston

Numerade Educator

Problem 45

In the following exercises, solve the systems of equations by substitution.
$$
\left\{\begin{array}{l}
y=-\frac{2}{3} x+5 \\
2 x+3 y=11
\end{array}\right.
$$

Teresa Fuston

Numerade Educator

Problem 46

In the following exercises, solve the systems of equations by elimination.
$$
\left\{\begin{array}{l}
5 x+2 y=2 \\
-3 x-y=0
\end{array}\right.
$$

Erika Bustos

Numerade Educator

Problem 47

In the following exercises, solve the systems of equations by elimination.
$$
\left\{\begin{array}{l}
6 x-5 y=-1 \\
2 x+y=13
\end{array}\right.
$$

Erika Bustos

Numerade Educator

Problem 48

In the following exercises, solve the systems of equations by elimination.
$$
\left\{\begin{array}{l}
2 x-5 y=7 \\
3 x-y=17
\end{array}\right.
$$

Erika Bustos

Numerade Educator

Problem 49

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

Erika Bustos

Numerade Educator

Problem 50

In the following exercises, solve the systems of equations by elimination.
$$
\left\{\begin{array}{l}
3 x-5 y=-9 \\
5 x+2 y=16
\end{array}\right.
$$

Erika Bustos

Numerade Educator

Problem 51

In the following exercises, solve the systems of equations by elimination.
$$
\left\{\begin{array}{l}
4 x-3 y=3 \\
2 x+5 y=-31
\end{array}\right.
$$

Erika Bustos

Numerade Educator

Problem 52

In the following exercises, solve the systems of equations by elimination.
$$
\left\{\begin{array}{l}
3 x+8 y=-3 \\
2 x+5 y=-3
\end{array}\right.
$$

Erika Bustos

Numerade Educator

Problem 53

In the following exercises, solve the systems of equations by elimination.
$$
\left\{\begin{array}{l}
11 x+9 y=-5 \\
7 x+5 y=-1
\end{array}\right.
$$

Erika Bustos

Numerade Educator

Problem 54

In the following exercises, solve the systems of equations by elimination.
$$
\left\{\begin{array}{l}
3 x+8 y=67 \\
5 x+3 y=60
\end{array}\right.
$$

Erika Bustos

Numerade Educator

Problem 55

In the following exercises, solve the systems of equations by elimination.
$$
\left\{\begin{array}{l}
2 x+9 y=-4 \\
3 x+13 y=-7
\end{array}\right.
$$

Erika Bustos

Numerade Educator

Problem 56

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

Erika Bustos

Numerade Educator

Problem 57

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

Erika Bustos

Numerade Educator

Problem 58

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

Erika Bustos

Numerade Educator

Problem 59

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

Erika Bustos

Numerade Educator

Problem 60

In the following exercises, solve the systems of equations by elimination.
$$
\left\{\begin{array}{l}
2 x+y=3 \\
6 x+3 y=9
\end{array}\right.
$$

Erika Bustos

Numerade Educator

Problem 61

In the following exercises, solve the systems of equations by elimination.
$$
\left\{\begin{array}{l}
x-4 y=-1 \\
-3 x+12 y=3
\end{array}\right.
$$

Erika Bustos

Numerade Educator

Problem 62

In the following exercises, solve the systems of equations by elimination.
$$
\left\{\begin{array}{l}
-3 x-y=8 \\
6 x+2 y=-16
\end{array}\right.
$$

Erika Bustos

Numerade Educator

Problem 63

In the following exercises, solve the systems of equations by elimination.
$$
\left\{\begin{array}{l}
4 x+3 y=2 \\
20 x+15 y=10
\end{array}\right.
$$

Erika Bustos

Numerade Educator

Problem 64

In the following exercises, decide whether it would be more convenient to solve the system of equations by substitution or elimination.
(a) $\left\{\begin{array}{l}8 x-15 y=-32 \\ 6 x+3 y=-5\end{array}\right.$
(b) $\left\{\begin{array}{l}x=4 y-3 \\ 4 x-2 y=-6\end{array}\right.$

Edward Downes

Numerade Educator

Problem 65

In the following exercises, decide whether it would be more convenient to solve the system of equations by substitution or elimination.
(a) $\left\{\begin{array}{l}y=7 x-5 \\ 3 x-2 y=16\end{array}\right.$
(b) $\left\{\begin{array}{l}12 x-5 y=-42 \\ 3 x+7 y=-15\end{array}\right.$

Edward Downes

Numerade Educator

Problem 66

In the following exercises, decide whether it would be more convenient to solve the system of equations by substitution or elimination.
(a) $\left\{\begin{array}{l}y=4 x+9 \\ 5 x-2 y=-21\end{array}\right.$
(b) $\left\{\begin{array}{l}9 x-4 y=24 \\ 3 x+5 y=-14\end{array}\right.$

Edward Downes

Numerade Educator

Problem 67

In the following exercises, decide whether it would be more convenient to solve the system of equations by substitution or elimination.
(a) $\left\{\begin{array}{l}14 x-15 y=-30 \\ 7 x+2 y=10\end{array}\right.$
(b) $\left\{\begin{array}{l}x=9 y-11 \\ 2 x-7 y=-27\end{array}\right.$

Edward Downes

Numerade Educator

Problem 68

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

Problem 69

Solve the system of equations by substitution and explain all your steps in words: $\left\{\begin{array}{l}3 x+y=12 \\ x=y-8\end{array}\right.$.

Satyam Gupta

Numerade Educator

Problem 70

Solve the system of equations by elimination and explain all your steps in words: $\left\{\begin{array}{l}5 x+4 y=10 \\ 2 x=3 y+27\end{array}\right.$.

Daniel Carr

Numerade Educator

Problem 71

Solve the system of equations $\left\{\begin{array}{l}x+y=10 \\ x-y=6\end{array}\right.$
(a) by graphing
(b) by substitution
(c) Which method do you prefer? Why?

Satyam Gupta

Numerade Educator