Systems of Two Equations

Kuta Software - Infinite Algebra 2 Name___________________________________
Date________________ Period____
Systems of Two Equations

Solve each system by graphing. 2) y = x + 2
x = −3
1) y = −3x + 4
y = 3x − 2

5 5
4 4
3 3
2 2
1 1

−5 −4 −3 −2 −1 0 12345 −5 −4 −3 −2 −1 0 12345
−1 −1
−2 −2
−3 −3
−4 −4
−5 −5

3) x − y = 3 4) 4x + y = 2
7x − y = −3 x− y=3

5 5
4 4
3 3
2 2
1 1

−5 −4 −3 −2 −1 0 12345 −5 −4 −3 −2 −1 0 12345
−1 −1
−2 −2
−3 −3
−4 −4
−5 −5

Solve each system by substitution. 6) 4x + 2y = 10
x − y = 13
5) y = 4x − 9
y=x−3 8) x + 7y = 0
2x − 8y = 22
7) y = −5
5x + 4 y = −20

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9) 6x + 8 y = −22 10) −7x + 2y = 18
y = −5 6x + 6y = 0

11) 7x + 2 y = −19 12) 3x − 5y = 17
−x + 2 y = 21 y = −7

13) −7x + 4 y = 24 14) 4x − y = 20
4x − 4y = 0 −2x − 2y = 10

Solve each system by elimination. 16) 6x − 12 y = 24
15) 8x − 6 y = −20 −x − 6y = 4

−16x + 7 y = 30 18) −24 − 8x = 12 y
57
17) −8x − 10 y = 24
6x + 5y = 2 1+ y=− x
9 18
19) −4 y − 11x = 36
20 = −10x − 10 y 20) −9 + 5 y = −4x
−11x = −20 + 9 y

21) 0 = −2 y + 10 − 6x 22) −16y = 22 + 6x
14 − 22 y = 18x −11 y − 4x = 15

23) −16 + 20x − 8 y = 0 5 11
36 = −18 y − 22x 24) − − x = − y

77
2y = 7 + 5x

Critical thinking questions:

25) Write a system of equations with the solution (4, −3).

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Kuta Software - Infinite Algebra 2 Name___________________________________
Date________________ Period____
Systems of Two Equations
2) y = x + 2
Solve each system by graphing. x = −3

1) y = −3x + 4
y = 3x − 2

5 5
4 4
3 3
2 2
1 1

−5 −4 −3 −2 −1 0 12345 −5 −4 −3 −2 −1 0 12345
−1 −1
−2 −2
−3 −3
−4 −4
−5 −5

(1, 1) (−3, −1)

3) x − y = 3 4) 4x + y = 2
7x − y = −3 x− y=3

5 5
4 4
3 3
2 2
1 1

−5 −4 −3 −2 −1 0 12345 −5 −4 −3 −2 −1 0 12345
−1 −1
−2 −2
−3 −3
−4 −4
−5 −5

(−1, −4) (1, −2)

Solve each system by substitution. 6) 4x + 2y = 10
x − y = 13
5) y = 4x − 9
y=x−3 (6, −7)

(2, −1) 8) x + 7y = 0
2x − 8y = 22
7) y = −5
(7, −1)
5x + 4 y = −20

(0, −5)

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9) 6x + 8 y = −22 10) −7x + 2y = 18
y = −5 6x + 6y = 0

(3, −5) (−2, 2)

11) 7x + 2 y = −19 12) 3x − 5y = 17
−x + 2 y = 21 y = −7

(−5, 8) (−6, −7)

13) −7x + 4 y = 24 14) 4x − y = 20
4x − 4y = 0 −2x − 2y = 10

(−8, −8) (3, −8)

Solve each system by elimination. 16) 6x − 12 y = 24
−x − 6y = 4
15) 8x − 6 y = −20
−16x + 7 y = 30 (2, −1)

(−1, 2) 18) −24 − 8x = 12 y
57
17) −8x − 10 y = 24
6x + 5y = 2 1+ y=− x
9 18
(7, −8)
(6, −6)
19) −4 y − 11x = 36
20 = −10x − 10 y 20) −9 + 5 y = −4x
−11x = −20 + 9 y
(−4, 2)
(1, 1)

21) 0 = −2 y + 10 − 6x 22) −16 y = 22 + 6x
14 − 22 y = 18x −11 y − 4x = 15

(2, −1) (−1, −1)

23) −16 + 20x − 8 y = 0 5 11
36 = −18 y − 22x 24) − − x = − y

(0, −2) 77
2y = 7 + 5x

(−3, −4)

Critical thinking questions:

25) Write a system of equations with the solution (4, −3).

Many answers. Ex: x + y = 1, 2x + y = 5

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