Quiz next Friday, March 20th

Sections 1-0 to 1-2

20 minutes – at the beginning of class

Review Homework

•Page 45-46

#1) (2,0)

#2) (-1,-1)

#3) IMS

#4) NS

#5

(5,4) 0

(10,8) X

Solving Linear Systems by Substitution page 47

Method to solve Linear Equations using substitution 1.Solve one of the equations for one of its

variables2.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.

Already in slope intercept form• y=4x-8 and y=2x+10If 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 = +82x = 18, x = 9

Solve by Substitution

y=4x-8 and y=2x+10x = 9, substitute the value of x into one of the

equations to solve for y.y= 4(9) -8 = 36-8 = 28Check (9,28) in the other equation

y = 2x+ 1028 = 2(9) + 10

28 = 28

Solve by substitution

y=x-2 and 2x+2y = 4 substitute x-2 for y in the second equation2x + 2(x-2) =4 (simplify)2x + 2x – 4 = 44x = 0 x = 0y = x – 2 y = 0 -2 = -2 (0,-2)2(0) + 2(-2) = 4 not true…… hmmm… mistake4x=8 x = 2 y = 2-2, y = 0 (2,0) 2(2) + 2(0) = 4

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 y2y=14-4x, y=7-2x substitute 7-2x for y in the other equation7x – 3(7-2x) = -8 distributive property7x – 21 +6x =-813 x = 13 x = 1y = 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)

Practice

•Page 49

page 491) -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

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.

4x + 3y = 78x - 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 x4(1) + 3y = 7 , 3y = 3, y = 1,

check using the other equation8(1) – 3(1) = 5 5 = 5so the solution is (1,1)

3x + 2y = -9-10x + 5y = -5You 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.

30x + 20y =-90-30x +15y = -15 35y = -105 y = -3Substitute 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 equation3(-1) + 2(-3) = -9-3 + -6 = -9 -9 = -9

Practice

• Page 54

page 541) x – y = 4 + x + y = 12 2x = 16 x = 8 8-y=4; y=4 (8,4)check x+y=128+4=1212=12

2) 5c+2d=7 +3c-d=13multiply 2nd by 2 5c+2d=7 6c-2d=26 11c = 33; c=35(3)+2d=7; d=-4(3,-4) check 3c-d=133(3)-(-4)=1313=13

Homework

Page 50-51 substitution , 55-56, 가감법