Chapter 9 Unit Question How do we solve linear systems?

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Presentation transcript:

Chapter 9 Unit Question How do we solve linear systems?

Get your Learning Logs Warm-up to follow…

Solve using Addition

Problems? Let’s talk about it...

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

Homework Clicky

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 = a) Multiply, if needed -3x + -3y = -15 3x + 4y = 12

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 = x = -2 2 x = -1 Step 1a multiply by 2 2x + 3y = 4 -2x + 8y = 18

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

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

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 = x + y = x = x = $6.00 4x + 5y = (6) + 5y = Stapler + 1 Paper = $ y = Multiply 2 nd equation by -5 4x + 5y = x – 5y = y = y = $5.50

Homework HoffmaSheet 9 – 5