To review these concepts, go to Graphing Systems of Linear Equations and Inequalities Study Guide.
Practice
Determine if the following equations are linear equations.
 5x + y = 13
 6x – 3y = 8
 y = 12
 x + y^{2} = 11
 3x + 2xy – 4y = 5
 y^{2} + 5x + 6 = 0
 x + y^{3} = 11
 3x + 2y + 5 = x – y + 7
Graph the systems of equations and state the solution(s).

y = 2x + 4
y = 3x + 3

y = 2x + 2

y = –4x + 1
y = 4x–1

2y + 3x = 12
6y – 2x = 4

5y – 10x = 15
7y + 14x = 21

9x – 3y = 18
4x – y = 16

–28x + 4y = 32
16x – 16y= –48

–9x + 6y= 12
30x – 15y = 15

200y – 400x = –600
75y + 150x = 300

–17x – 17y = 17
–19x – 19y = 19
Without graphing the system, determine the number of solutions the system will have.

y = 3x – 5
y = 3x + 2

x + 3y = 10
2x + 6y = 20

3y – 2x = 6
2y – 3x = 4

2x + 3y = 6
3x – y = 2

y + 3 = 3x + 5
3y = 9x

3x + y = 6
3x – y= 6

4x – 3y = 12
–4x + 3y = –12

3x + 3y = 15
–2x – 2y = 8
Solve the systems of inequalities graphically.

y > 4
y < x + 2

y ≥ 5
x ≤ 2

y < x + 2
y < –x + 4

x + y > 5
–2x + y > 3

x ≥ 0
y ≥ 0
y ≤ –2x + 10

y = x + 2
y = –x+ 4

2y – x= 2
3x + y = 8

4y = – 7(x + 4)
4y = x + 4

y – x = 5 – x
–4y = 8 – 7x

2y = 6x + 14
4y = x – 16

2x + y = 4
3(y + 9) = 7x

y = x + 9
4y = 16 – x

4
x – 5y = 5 5y = 20 – x

6y = 9(x – 6)
3(2y + 5x) = –6

15y = 6(3x + 15)
y = 6(1 – x)

3y = 6x + 6
5y = 10(x – 5)

3(2x + 3y) = 63
27y = 9(x – 6)

x – 20 = 5y
10y = 8x + 20

3x + 4y = 12

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