Systems

You can open your book to page 417 to refresh your memory as you start your warm-up. The information presented in this lesson will

be included in sections 9-2, 9-4, and 9-5.

Please take 5 minutes to work on the following problems…

1. x+y= 154x+3y= 38

2. 6c+7d= -156c-2d= 12

3. 3a+4b= 25a+9b= 1

1) Solve one equation for one of the variables2) Substitute this expression in the other

equation and solve for the other variable3) Substitute this value in the equation in step

1 and solve4) Check the values in both equations

Example 1: 2x-3y=4x+4y= -9

1.) 2x-3y=4x= -9-4y

2.) 2(-9-4y)-3y=4y= -2

3.) x+4(-2)= -9x= -1

4.) 2(-1)-3(-2)=4 4=4 yes(-1)+4(-2)= -9 -9= -9

yesAnswer (-1,-2)

Use the 4 step process…

Solve one equation

Substitute and solve in other equation

Substitute this value in the equation in step 1 and solve

Check

Example 2: 2x-8y=6x-4y=8

1.) 2x-8y=6x=4y+8

2.) 2(4y+8)-8y=616=6 no

3.) No solution; special case where the variables cancel each other out and the 4 step process does not work.

Use the 4 step process…

Solve one equation

Substitute and solve in other equation

Substitute this value in the equation in step 1 and solve

Check

1. Add or subtract the equation to eliminate one variable

2. Solve the resulting equation for the other variable

3. Substitute in either original equation to find the value of the first variable

4. Check in both equations

Example 1: 2c+3d=0 + 5c-3d=21

1.) 7c=21 7 7

2.) c=3

3.) 2(3)+3d=06+3d=0d= -2

4.) 2(3)+3(-2)=00=0 yes

5(3)-3(-2)=21 21=21 yes

Answer (3,-2)

Add or subtract the equation to eliminate one

variable

Solve the resulting equation for the other variable

Substitute in either original equation to find the value of the first variable

Check in both equations

5 Step Addition and Subtraction Process Using Multiplication

Multiply one or both the equations so the absolute value of the coefficients of one of the variables are equal

Add or subtract the equation to eliminate one variable




• Example 2: 4x+5t=225x-t= 13

1.) 4x+5t=22

(5)5x-t= 13(5)

2.) 4x+5t=22

+ 25x-5t=653.) 29x=87

29 29 x=3

4.) 5(3)-t=13t=2

5.) 4(3)+5(2)=22 22=22 yes

5(3)-2=13 13=13 yes

Answer (2,3)

• Example 3: 6n+8c-4=09n+10c-7=0

1.) (3/2)6n+8c-4=0(3/2)

9n+10c-7=0

2.) 9n+12c-6=0-(9n+10c-7=0)

2c= -13.) 2 2 c= -1/24.) 6n+8(-1/2)-4=0

n= 4/35.) 6(4/3)+8(-1/2)-

4=0 0=0 yes

9(4/3)+10(-1/2)-7=0 0=0 yes

Answer (-1/2, 4/3)

5 Step Addition and Subtraction Process Using Multiplication

Multiply one or both the equations so the absolute value of the coefficients of one of the variables are equal

Add or subtract the equation to eliminate one variable




Please take 5 minutes to complete your assessment…

1.y/2= 2-x6x+3y= 12

2.5x-y= 123x+y= 4

3.4x-5y= 233x+10y= 31

-Remember…-To solve any system you must find the

value of one variable-After that you substitute that answer in

one equation to find the other variable-Finally you check your answers

(Important to have on foldable)

Systems

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