1. Warm-Up Solve the equation. 1. 6a – 3 + 2a = 13 2. 4(n + 2) – n = 11 3. One auto repair shop charges $30 for a diagnosis and $25 per hour for labor. Another auto repair shop only charges $35 per hour for labor. For how many hours are the total charges for both of the shops the same? a = 2 n = 1 3 hours 30 + 25x = 35x

2. Agenda for Thursday 11/29/12 Questions on solving using substitution More on Solving Linear Systems Using Substitution Assignment… Target 7a: I can solve linear systems by graphing, substitution, and elimination.

3. Daily Quiz Solve the linear system by using substitution. 1. 4x + 3y = 02. 8x – 4y = 32 y = -2x – 2 x = 3y + 9 (-3,4) (3,-2) 3. One auto repair shop charges $30 for a diagnosis and $25 per hour for labor. Another auto repair shop only charges $35 per hour for labor. For how many hours are the total charges for both of the shops the same? 3 hours 30 + 25x = 35x

4. Solving Linear Systems Using Substitution

5. Solving Linear Systems Using Substitution x – 2y = -6 4x + 6y = 4 Before you can use substitution, x or y needs to be alone in one of the equations. x = 2y – 6 4(2y – 6) + 6y = 4 8y – 24 + 6y = 4 14y – 24 = 4 +24 +24 14y = 28 14 14 y = 2 Plug 2y – 6 in for x. Solve for y. x = 2(2) – 6 x = -2 The solution is (-2,2) Plug 2 in for y. Solve for x.

6. Lets try another one together! -5x – y = 12 3x – 5y = 4 Get x or y alone in one of the equations. y = -5x – 12 3x – 5(-5x – 12) = 4 3x + 25x + 60 = 4 28x + 60 = 4 -60 -60 28x = -56 28 28 x = -2 y = -5(-2) – 12 y = -2 Plug -5x – 12 in for y. Solve for x. Plug -2 in for x. Solve for y. The solution is (-2,-2)

7. Try these… x – y = 3 x + 2y = -6 3x + y = -7 -2x + 4y = 0 x = y + 3 y = -3x – 7 (y + 3) + 2y = -6 3y + 3 = -6 -3 -3 3y = -9 3 3 y = -3 x = -3 + 3 x = 0 (0,-3) -2x + 4(-3x – 7) = 0 -2x – 12x – 28 = 0 -14x – 28 = 0 +28 +28 -14x = 28 -14 -14 x = -2 y = -3(-2) – 7 y = -1 (-2,-1)

8. A Word Problem! Last year, you mowed grass and shoveled snow for 12 households. You earned $225 for mowing a household’s lawn for an entire year and $200 for shoveling a household’s walk and driveway for an entire year. You earned a total of $2600 last year. How many households did you mow and shovel for last year? Step 1: Write a system of equations. x is mowing y is shoveling x + y = 12 225x + 200y = 2600 y = -x + 12 Step 2: Solve using substitution. 225x + 200(-x + 12) = 2600 225x – 200x + 2400 = 2600 25x + 2400 = 2600 25x = 200 x = 8 y = -8 + 12 y = 4 8 lawns mowed 4 walks & driveways shoveled

9. Agenda for Thursday 11/29/12 Assignment… –Pg. 439-440 Target 7a: I can solve linear systems by graphing, substitution, and elimination.