1. Quiz next Friday, March 20 th Sections 1-0 to 1-2 20 minutes – at the beginning of class

2. Review Homework Page 45-46

3. #1) (2,0)

4. #2) (-1,-1)

5. #3) IMS

6. #4) NS

7. #5 (5,4) 0 (10,8) X

8. Solving Linear Systems by Substitution page 47 Method to solve Linear Equations using substitution 1.Solve one of the equations for one of its variables 2.Substitute this expression into the other equation and solve for the other variable. 3.Substitute this value into the revised first equation and solve. 4.Check the solution pair in each of the original equations.

9. Already in slope intercept form y=4x-8 and y=2x+10 If both are already solved for one variable, set them equal to each other. Since both 4x-8 and 2x+10 are equal to y, then they are equal to each other. (get all variables to one side & constants to the other) 4x-8 = 2x+10 -2x = -2x 2x -8 = 10 +8 = +8 2x = 18, x = 9

10. Solve by Substitution y=4x-8 and y=2x+10 x = 9, substitute the value of x into one of the equations to solve for y. y= 4(9) -8 = 36-8 = 28 Check (9,28) in the other equation y = 2x+ 10 28 = 2(9) + 10 28 = 28

11. Solve by substitution y=x-2 and 2x+2y = 4 substitute x-2 for y in the second equation 2x + 2(x-2) =4 (simplify) 2x + 2x – 4 = 4 4x = 0 x = 0 y = x – 2 y = 0 -2 = -2 (0,-2) 2(0) + 2(-2) = 4 not true…… hmmm… mistake 4x=8 x = 2 y = 2-2, y = 0 (2,0) 2(2) + 2(0) = 4

12. Neither equation is in slope intercept form 4x+2y=14 and 7x-3y=-8 Solve either for one of the variables and substitute it into the other equation. Solve 4x +2y =14 for y 2y=14-4x, y=7-2x substitute 7-2x for y in the other equation 7x – 3(7-2x) = -8 distributive property 7x – 21 +6x =-8 13 x = 13 x = 1 y = 7 – 2(1) = 5 (1,5) 4(1) + 2(5) =14 (always substitute into an original equation, not the one you simplified (y=7-2x)

13. Practice Page 49

14. page 49 1)-3n-6 = n-4 -2 = 4n n=-0.5 c(n)=-3(-0.5)-6 c(n) =-4.5 (-0.5,-4.5) check c(n)=n-4 -4.5=-0.5-4 -4.5=-4.5 2) -4x+12.5=0.25x+4 -4.25x =-8.5 x = 2 y=-4x+12.5 y=-8+12.5 = 4.5 (2,4.5) check y=0.25x+4 4.5 =0.25(2)+4 4.5=4.5

15. Solving Systems using Elimination 가감법 (Linear Combination) page 52 The goal is to use addition/subtraction and multiplication/division to combine the two linear equations to eliminate one variable so you can solve for the other variable. You can then substitute the value into one of the original equations to find the other value and then check the answers in the other original equation.

16. 4x + 3y = 7 8x - 3y = 5 If we add the two equations together, the variable y will be eliminated. 12 x = 12, x = 1 Choose either equation to find the value of y by substituting the value of x 4(1) + 3y = 7, 3y = 3, y = 1, check using the other equation 8(1) – 3(1) = 5 5 = 5 so the solution is (1,1)

17. 3x + 2y = -9 -10x + 5y = -5 You can not eliminate a variable by adding or subtracting, so you need to multiply one or both equations so you can add them together to eliminate a variable Arrow Method (change one of the signs) 10 3x + 2y = -9  30x + 20y =-90 3-10x + 5y = -5  -30x +15y = -15 Copy the coefficients from one end of the arrow to the other, changing one of the signs.

18. 30x + 20y =-90 -30x +15y = -15 35y = -105 y = -3 Substitute back into one of the original equations 3x + 2y = -9 -10x + 5y = -5 -10x + 5(-3) = -5 -10x =10, x = -1 Substitute (-1,-3) into the other equation 3(-1) + 2(-3) = -9 -3 + -6 = -9 -9 = -9

19. Practice Page 54

20. page 54 1)x – y = 4 + x + y = 12 2x = 16 x = 8 8-y=4; y=4 (8,4) check x+y=12 8+4=12 12=12 2)5c+2d=7 +3c-d=13 multiply 2 nd by 2 5c+2d=7 6c-2d=26 11c = 33; c=3 5(3)+2d=7; d=-4 (3,-4) check 3c-d=13 3(3)-(-4)=13 13=13

21. Homework Page 50-51 substitution, 55-56, 가감법