Systems of Two Equations - Kuta Software

Kuta Software - Infinite Algebra 2

Name___________________________________

Systems of Two Equations

Date________________ Period____

Solve each system by graphing.

1) y = ?3 x + 4

y = 3x ? 2

?5

?4

?3

?2

2) y = x + 2

x = ?3

5

5

4

4

3

3

2

2

1

1

?1 0

?1

1

2

3

4

5

?4

?3

?2

?4

?3

?2

?1 0

?1

?2

?2

?3

?3

?4

?4

?5

?5

3) x ? y = 3

7 x ? y = ?3

?5

?5

1

2

3

4

5

1

2

3

4

5

4) 4 x + y = 2

x? y=3

5

5

4

4

3

3

2

2

1

1

?1 0

?1

1

2

3

4

5

?5

?4

?3

?2

?1 0

?1

?2

?2

?3

?3

?4

?4

?5

?5

Solve each system by substitution.

5) y = 4 x ? 9

y=x?3

6) 4 x + 2 y = 10

x ? y = 13

7) y = ?5

5 x + 4 y = ?20

8) x + 7 y = 0

2 x ? 8 y = 22

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Worksheet by Kuta Software LLC

9) 6 x + 8 y = ?22

y = ?5

10) ?7 x + 2 y = 18

6x + 6 y = 0

11) 7 x + 2 y = ?19

? x + 2 y = 21

12) 3 x ? 5 y = 17

y = ?7

13) ?7 x + 4 y = 24

4x ? 4 y = 0

14) 4 x ? y = 20

?2 x ? 2 y = 10

Solve each system by elimination.

15) 8 x ? 6 y = ?20

?16 x + 7 y = 30

16) 6 x ? 12 y = 24

?x ? 6 y = 4

17) ?8 x ? 10 y = 24

6x + 5 y = 2

18) ?24 ? 8 x = 12 y

5

7

1+ y=? x

9

18

19) ?4 y ? 11 x = 36

20 = ?10 x ? 10 y

20) ?9 + 5 y = ?4 x

?11 x = ?20 + 9 y

21) 0 = ?2 y + 10 ? 6 x

14 ? 22 y = 18 x

22) ?16 y = 22 + 6 x

?11 y ? 4 x = 15

23) ?16 + 20 x ? 8 y = 0

36 = ?18 y ? 22 x

24) ?

5 11

?

x = ?y

7

7

2 y = 7 + 5x

Critical thinking questions:

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

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Worksheet by Kuta Software LLC

Kuta Software - Infinite Algebra 2

Name___________________________________

Systems of Two Equations

Date________________ Period____

Solve each system by graphing.

1) y = ?3 x + 4

y = 3x ? 2

?5

?4

?3

?2

2) y = x + 2

x = ?3

5

5

4

4

3

3

2

2

1

1

?1 0

?1

1

2

3

4

5

?5

?3

?2

?1 0

?1

?2

?3

?3

?4

?4

?5

?5

1

2

3

4

5

1

2

3

4

5

(?3, ?1)

3) x ? y = 3

7 x ? y = ?3

?4

?3

?2

(1, 1)

?5

?4

?2

4) 4 x + y = 2

x? y=3

5

5

4

4

3

3

2

2

1

1

?1 0

?1

1

2

3

4

5

?5

?4

?3

?2

?1 0

?1

?2

?2

?3

?3

?4

?4

?5

?5

(?1, ?4)

(1, ?2)

Solve each system by substitution.

5) y = 4 x ? 9

y=x?3

6) 4 x + 2 y = 10

x ? y = 13

(2, ?1)

(6, ?7)

7) y = ?5

5 x + 4 y = ?20

(0, ?5)

8) x + 7 y = 0

2 x ? 8 y = 22

(7, ?1)

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Worksheet by Kuta Software LLC

9) 6 x + 8 y = ?22

y = ?5

(3, ?5)

11) 7 x + 2 y = ?19

? x + 2 y = 21

(?5, 8)

13) ?7 x + 4 y = 24

4x ? 4 y = 0

(?8, ?8)

Solve each system by elimination.

10) ?7 x + 2 y = 18

6x + 6 y = 0

(?2, 2)

12) 3 x ? 5 y = 17

y = ?7

(?6, ?7)

14) 4 x ? y = 20

?2 x ? 2 y = 10

(3, ?8)

15) 8 x ? 6 y = ?20

?16 x + 7 y = 30

16) 6 x ? 12 y = 24

?x ? 6 y = 4

(?1, 2)

17) ?8 x ? 10 y = 24

6x + 5 y = 2

(7, ?8)

(2, ?1)

18) ?24 ? 8 x = 12 y

5

7

1+ y=? x

9

18

(6, ?6)

19) ?4 y ? 11 x = 36

20 = ?10 x ? 10 y

20) ?9 + 5 y = ?4 x

?11 x = ?20 + 9 y

(?4, 2)

21) 0 = ?2 y + 10 ? 6 x

14 ? 22 y = 18 x

(1, 1)

22) ?16 y = 22 + 6 x

?11 y ? 4 x = 15

(2, ?1)

23) ?16 + 20 x ? 8 y = 0

36 = ?18 y ? 22 x

(?1, ?1)

5 11

?

x = ?y

7

7

2 y = 7 + 5x

24) ?

(0, ?2)

(?3, ?4)

Critical thinking questions:

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

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

Create your own worksheets like this one with Infinite Algebra 2. Free trial available at

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Worksheet by Kuta Software LLC

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