Warmup 6 3 Elimination Using Addition and Subtraction

Warm-up •

6. 3 : Elimination Using Addition and Subtraction

Steps for Solving by Elimination with Addition/Subtraction 1) Arrange the equations in standard form. 2) Add or subtract the equations to eliminate one variable and solve. 3) Substitute the value from Step 2 into one of the equations and solve for the other variable. 4) Check your answer.

Example 1 Use elimination to solve the system of equations. a) – 3 x + 4 y = 12 3 x – 6 y = 18

Example 1 Use elimination to solve the system of equations. b) 3 x – 5 y = 1 2 x + 5 y = 9

Example 2: Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Write a system of linear equations and then use elimination to solve it and find the numbers.

Example 3 Use elimination to solve the system of equations. a) 4 x – 28 = – 2 y 4 x – 3 y = 18

Example 3 Use elimination to solve the system of equations. b) 9 x – 2 y = 30 – 2 y + x = 14

Example 4 a) A hardware store earned $956. 50 from renting ladders and power tools last week. The store charged 36 days for ladders and 85 days for power tools. This week the store charged 36 days for ladders, 70 days for power tools, and earned $829. How much does the store charge per day for ladders and for power tools?

Example 4 b) For a school fundraiser, Marcus and Anisa participated in a walk-a-thon. In the morning, Marcus walked 11 miles and Anisa walked 13. Together they raised $523. 50. After lunch, Marcus walked 14 miles and Anisa walked 13. In the afternoon they raised $586. 50. How much did each raise per mile of the walk-a-thon?

Exit Slip Solve the system using elimination: -2 x + 3 y = 6 2 x - y = 2

Homework Page 354: 8 -14 even, 20, 22, 23, 30