Systems of Equations - Linear Combination

Systems of Equations - Linear Combination

Solve each system. Show all work. No graphing calculators!!

1. x – 3y = -13 2. x + y = 10

-x + 4y = 15 x – y = 2

3. 5x + 2y = -8 4. 3x + 2y = 9

3x – 2y = -8 3x + 4y = 3

5. 4x + 3y = 19 6. 2x – y = -6

7x – 6y = -23 2x + 3y = 14

7. 3t – 8z = 34 8. 2c – 7d = 41

7t + 4z = -34 6c + 5d = -7

9. Mrs. Lewis is celebrating Euclid’s birthday by having a birthday party for her two Algebra classes. She orders 3 pizzas and 3 bottles of soda for $21 for her 2nd block class and 4 pizzas and 6 bottles of soda for $30 for her 4th block class. How much does each pizza and each bottle of soda cost?

10. The cost of 3 pairs of shoes and 5 pair of shorts is $340. The cost of 1 pairs of shoes and 4 pair of shorts is $160. Find the cost of each pair of shoes and each pair of shorts.

Solve each system of equations below by graphing.

11.

12. y – 3x = -1

y = x + 3

13. 3x + y = 9

-2x + y = 1

Solve each system of equations below using the substitution method.

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14. x + 3y = 2

2x + 3y = 7

15. 3x – 2y = 5

x + 2y = 15

16. m – 4n = -5

m = 2n – 4

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Set up a system of equations for each problem and then solve using substitution or linear combination.

17. Kelly has 24 dimes and quarters worth $3.60. How many quarters does she have?

18. The length of a rectangle is 5 cm less than 3 times its width. If the perimeter is 70 cm, find the dimensions.

19. On a jury there are 3 fewer men than twice the number of women. If there were 2 more women on the jury, the number of men and women would be equal. How many men are on the jury?

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