1. Chapter 9 Unit Question How do we solve linear systems?

2. Get your Learning Logs Warm-up to follow…

3. Solve using Addition

4. Problems? Let’s talk about it...

5. Section 5 Essential Question How do we solve linear systems using multiplication?

6. Homework Clicky

7. Just like last time…with times! 1) Line up the equations 2)“Add” straight down EXAMPLE x + y = 5 3x + 4y = 12 y = -3 x + y = 5 So…the solution is the ordered pair…(8, -3) 3)Finish solving for the remaining variable 4)Substitute answer into an original equation x + -3 = 5 x = 8 +3 1a) Multiply, if needed -3x + -3y = -15 3x + 4y = 12

8. Find the 2 unknowns! 2x + 3y = 4 -x + 4y = 9 Step 1 … line ‘em up 11y = 22 Step 2 “add” straight down Step 4 substitute and solve for’x’ 11 y = 2 Step 3 solve for ‘y’ 2x + 3y = 4 2x + 3(2) = 4 (-1, 2) 2x + 6 = 4 -6 -6 2x = -2 2 x = -1 Step 1a multiply by 2 2x + 3y = 4 -2x + 8y = 18

9. Multiply the 1 st by 2 AND Multiply the 2 nd by 5… Find the 2 unknowns! 38x = -76 x = -2 38 4x + 5y = 7 4(-2) + 5y = 7 -8 +5y = 7 8x + 10y = 14 30x – 10y = -90 +8 5y = 15 5 y = 3 (-2, 3) 4x + 5y = 7 6x – 2y = -18

10. Multiply the 1 st by 3 AND Multiply the 2 nd by -2… Find the 2 unknowns a different way! 19y = 57 y = 3 19 4x + 5y = 7 4x + 5(3) = 7 4x +15 = 7 12x + 15y = 21 -12x + 4y = 36 -15 4x = -8 4 x = -2 (-2, 3) 4x + 5y = 7 6x – 2y = -18 EITHER WAY SAME ANSWER

11. The 8 th grade team spent $51.50 on 4 staplers and 5 boxes of paper… The 7 th grade team spent $65.50 on 10 staplers and 1 box of paper… What’s the cost of 1 stapler and 1 box of paper? Let x = cost of stapler y = cost of paper 4x + 5y = 51.50 10x + y = 65.50 -46x = -276.00 -46 x = $6.00 4x + 5y = 51.50 4(6) + 5y = 51.50 1 Stapler + 1 Paper = $11.50 -24 5y = 27.50 Multiply 2 nd equation by -5 4x + 5y = 51.50 -50x – 5y = -327.50 24 + 5y = 51.50 5 y = $5.50

12. Homework HoffmaSheet 9 – 5