Unit 10: Systems of Linear Equations/Inequalities

Name: ______Date: ______Color: ______Unit 10: Systems of Linear Equations/Inequalities Solve Linear Systems by Multiplying First

1. What is the least common multiple of 12 and 18? 36 2x – 3y = -4 2. Explain how to solve the linear system using the elimination method. 7x + 9y = -5 Multiply equation 1 by 3 and add to Equation 2. Then solve for x and substitute to find y. Solve the linear system using elimination. 3. 4x – 3y = 8 4. -2x – 5y = 9 5. 7x – 6y = -1 5x – 2y = -11 3x + 11y = 4 5x – 4y = 1 (-7, -12) (-17, 5) (5, 6) 6. 3x + 2y = 4 7. 4x – 5y = 18 8. 8x – 9y = -15 2y = 8 – 5x 3x = y + 11 -4x = 19 + y 4 10 5 1 (2, -1) (3 , - ) (-4 , -2 ) 11 11 22 11 9. 0.3x + 0.1y = -0.1 10. 4.4x – 3.6y = 7.6 11. 3x – 2y = -20 -x + y = 3 x – y = 1 x + 1.2y = 6.4 (-1, 2) (5, 4) (-2, 7) 12. 0.2x – 1.5y = -1 13. 1.5x – 3.5y = -5 14. 4.9x + 2.4y = 7.4 x – 4.5y = 1 -1.2x + 2.5y = 1 0.7x + 3.6y = -2.2 (10, 2) (20, 10) (2, -1) 15. A rectangle has a perimeter of 18 inches. A new rectangle is formed by doubling the width w and tripling the length ℓ, as shown. The new rectangle has P = 46 in. 2w a perimeter P of 46 inches. a. Write and solve a system of linear equations to find the length and width of the original rectangle. 2ℓ + 2x = 18 3ℓ 3(2ℓ) + 2(2w) = 46; 6ℓ + 4w = 46 b. Find the length and width of the new rectangle. Length = 15 inches; Width = 8 inches

16. The table shows the number of apples needed to make the apple pies and applesauce sold at a farm store. During a recent apply picking at the farm store. During a recent apple picking at the farm, 169 Granny Smith apples and 95 Golden Delicious apples were picked. How many apple pies and batches of applesauce can be made if every apple is used?

Type of apple Granny Smith Golden Delicious Needed for a pie 5 3 Needed for a batch of applesauce 4 2 p = pies a = applesauce 5p + 4a = 169 3p + 2a = 95 Pies = 21; Batches of Applesauce = 16 17. Tickets for admission to a high school football game cost $3 for students and $5 for adults. During one game, $2995 was collected from the sale from 729 tickets. a. Write and solve a system of linear equations to find the number of tickets sold to students and the number of tickets sold to adults. s = student tickets a = adult tickets 3s + 5a = 2995 s + a = 729 325 student tickets and 404 adult tickets b. Graph the system of linear equations. Use the graph to determine whether your answer to part (a) is reasonable.

18. A dim sum restaurant offers two sizes of dishes; small and large. All small dishes cost the same and all large dishes cost the same. The bills show 3 small 4 small the cost of the food before the tip is included. 5 large 3 large What will 3 small and 2 large dishes cost before the tip is included? Explain. $28.20 $23.30 s = small L = large 3s + 5L = 28.20 4s + 3L = 23.30 Small dish = $2.90 and a large dish = $3.90 3(2.90) + 2(3.90) = 16.50