Infinite Algebra 1 - Final Review - Systems

Algebra 1

Name___________________________________ ID: 1

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Final Review - Systems

Date________________ Period____

Solve each system by graphing. 2) x = -4 5 y= x+3 4

4 1) y = - x + 2 3 1 y=- x-1 3

y 5

y 5

4

4

3

3

2

2

1

1

-5

-4

-3

-2

-1

1

2

3

4

5 x

1

2

3

4

5 x

-1 -5

-4

-3

-2

-1

1

2

3

4

5 x

-1

-2

-2

-3

-3

-4

-4

-5

-5

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

4) y = x - 3 y = -2 y

-5

-4

-3

-2

y

5

5

4

4

3

3

2

2

1

1

-1

1

2

3

4

5 x

-5

-4

-3

-2

-1

-1

-1

-2

-2

-3

-3

-4

-4

-5

-5

Worksheet by Kuta Software LLC

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5) x - y = 1 3x + 2 y = 18 y 10 8 6 4 2 -10

-8

-6

-4

-2

2

4

6

8

10 x

-2 -4 -6 -8 -10

Solve each system (substitution). 6) y = x - 3 y = 4x - 12

7) y = x - 8 y = -4x + 12

8) y = -4x + 5 3x + 4 y = 7

9) -x - 2 y = 5 y = 3x - 6

Worksheet by Kuta Software LLC

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10) -6x - 4 y = -22 x + 2y = 5

11) 5x - 7 y = -17 y=1

Solve each system (elimination). 12) -x - 3 y = -7 x + 5 y = 11

13) -3x + 3 y = 9 4x - 3 y = -14

14) 5x - 2 y = -3 5x - 2 y = -10

15) -2x + 2 y = -22 -2x + y = -20

16) 7x - 6 y = -7 -14x + 7 y = -21

17) 8x + 12 y = 28 4x + 6 y = 14

18) -6x - 8 y = 4 -5x - 5 y = 0

19) -4x - 4 y = -24 10x - 5 y = -15

Worksheet by Kuta Software LLC

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20) The sum of two numbers is 11. Their difference is 1. Find the numbers.

21) Jacob and Maria each improved their yards by planting daylilies and ivy. They bought their supplies from the same store. Jacob spent $54 on 2 daylilies and 6 pots of ivy. Maria spent $19 on 2 daylilies and 1 pot of ivy. Find the cost of one daylily and the cost of one pot of ivy.

22) When you reverse the digits in a certain two-digit number you increase its value by 18. What is the number if the sum of its digits is 4?

23) Natalie and Sumalee are selling pies for a school fundraiser. Customers can buy apple pies and blackberry pies. Natalie sold 2 apple pies and 11 blackberry pies for a total of $206. Sumalee sold 6 apple pies and 10 blackberry pies for a total of $204. Find the cost each of one apple pie and one blackberry pie.

Worksheet by Kuta Software LLC

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Algebra 1

Name___________________________________ ID: 1

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Final Review - Systems

Date________________ Period____

Solve each system by graphing. 2) x = -4 5 y= x+3 4

4 1) y = - x + 2 3 1 y=- x-1 3

y 5

y 5

4

4

3

3

2

2

1

1

-5

-4

-3

-2

-1

1

2

3

4

5 x

1

2

3

4

5 x

-1 -5

-4

-3

-2

-1

1

2

3

4

5 x

-1

-2

-2

-3

-3

-4

-4

-5

-5

(-4, -2)

(3, -2)

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

4) y = x - 3 y = -2 y

-5

-4

(1, 3)

-3

-2

y

5

5

4

4

3

3

2

2

1

1

-1

1

2

3

4

5 x

-5

-4

-3

-2

-1

-1

-1

-2

-2

-3

-3

-4

-4

-5

-5

(1, -2)

Worksheet by Kuta Software LLC

-1-

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5) x - y = 1 3x + 2 y = 18 y 10 8 6 4 2 -10

-8

-6

-4

-2

2

4

6

8

10 x

-2 -4 -6 -8 -10

(4, 3)

Solve each system (substitution). 6) y = x - 3 y = 4x - 12

7) y = x - 8 y = -4x + 12

(3, 0)

(4, -4)

8) y = -4x + 5 3x + 4 y = 7

9) -x - 2 y = 5 y = 3x - 6

(1, 1)

(1, -3)

Worksheet by Kuta Software LLC

-2-

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10) -6x - 4 y = -22 x + 2y = 5

11) 5x - 7 y = -17 y=1

(3, 1)

(-2, 1)

Solve each system (elimination). 12) -x - 3 y = -7 x + 5 y = 11

13) -3x + 3 y = 9 4x - 3 y = -14

(1, 2)

14) 5x - 2 y = -3 5x - 2 y = -10

(-5, -2)

15) -2x + 2 y = -22 -2x + y = -20

(9, -2)

No solution

16) 7x - 6 y = -7 -14x + 7 y = -21

17) 8x + 12 y = 28 4x + 6 y = 14

(5, 7)

18) -6x - 8 y = 4 -5x - 5 y = 0

Infinite number of solutions

19) -4x - 4 y = -24 10x - 5 y = -15

(2, -2)

(1, 5)

Worksheet by Kuta Software LLC

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20) The sum of two numbers is 11. Their difference is 1. Find the numbers. 5 and 6

21) Jacob and Maria each improved their yards by planting daylilies and ivy. They bought their supplies from the same store. Jacob spent $54 on 2 daylilies and 6 pots of ivy. Maria spent $19 on 2 daylilies and 1 pot of ivy. Find the cost of one daylily and the cost of one pot of ivy. daylily: $6, pot of ivy: $7

22) When you reverse the digits in a certain two-digit number you increase its value by 18. What is the number if the sum of its digits is 4? 13

23) Natalie and Sumalee are selling pies for a school fundraiser. Customers can buy apple pies and blackberry pies. Natalie sold 2 apple pies and 11 blackberry pies for a total of $206. Sumalee sold 6 apple pies and 10 blackberry pies for a total of $204. Find the cost each of one apple pie and one blackberry pie. apple pie: $4, blackberry pie: $18

Worksheet by Kuta Software LLC

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