Solving Systems of Equations using Substitution

1 / 16

# Solving Systems of Equations using Substitution - PowerPoint PPT Presentation

Solving Systems of Equations using Substitution. HCPS Henrico County Public Schools Designed by Vicki Hiner- Godwin High School. Lesson Objective:. Solve systems of equations by substitution method. Assignment:. pp. 450-451 #5-30 Skip 9 Fractions on some of these, so don’t freak out. .

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Solving Systems of Equations using Substitution' - liza

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Solving Systems of Equations using Substitution

HCPS

Henrico County Public Schools

Designed by Vicki Hiner- Godwin High School

Lesson Objective:
• Solve systems of equations by substitution method.
Assignment:
• pp. 450-451 #5-30 Skip 9
• Fractions on some of these, so don’t freak out.
Solving Systems of Equations using Substitution

Steps:

1. Solve One equation for One variable( y= ; x= ; a=)

2. Substitute equation from step one into other equation (get an equation with only one variable)

3. Solve for the first variable.

4. Go back and use the found variable in step 3 to find second variable.

5. Check the solution in both equations of the system.

WHAT DO WE DO???? CLICK TO SEE AN EXAMPLE

GIVEN EXAMPLE:

y= 4x

3x+y=-21

STEP1:

STEP 2:

Substitute into second equation: 3x + y = -21 becomes:

GIVEN EXAMPLE:

y= 4x

3x+y=-21

STEP1:

STEP 2:

Substitute into second equation: 3x + y = -21 becomes:

3x +4x =-21

GIVEN EXAMPLE:

y= 4x

3x+y=-21

STEP 3: Solve for the variable

3x + 4x=-21

7x=-21

x=-3

GIVEN EXAMPLE:

y= 4x

3x+y=-21

STEP 4: Solve for the other variable use x=-3 and y=4x

y=4x and x = -3 therefore:

y=4(-3) or y = -12

Solution to the system is (-3,-12)

GIVEN EXAMPLE:

y= 4x

3x+y=-21

Check solution ( -3,-12)

y=4x

-12=4(-3)

-12=-12

3x+y=-21

3(-3)+(-12)=-21

-9+(-12)=-21

-21=-21

Solving Systems of Equations using Substitution

Review Steps --Questions?

Steps:

1. Solve One equation for One variable( y= ; x= ; a=)

2. Substitute equation from step one into other equation (get an equation with only one variable)

3. Solve for the first variable.

4. Go back and use the found variable in step 3 to find second variable.

5. Check the solution in both equations of the system.

GIVEN EXAMPLE:

x + y=10

5x - y=2

STEP1: Solve for y

x + y = 10

y = -x +10

STEP 2:

Substitute into second equation: 5x - y = 2 becomes:

GIVEN EXAMPLE:

x + y=10

5x - y=2

STEP1: Solve for Y

x + y = 10

y = -x +10

STEP 2:

Substitute into second equation: 5x - y = 2 becomes:

5x - (-x+10) = 2

GIVEN EXAMPLE:

x + y=10

5x - y=2

STEP 3: Solve for the variable

5x-(-x+10)=2

5x+x-10=2

6x-10=2

6x=12

x=2

GIVEN EXAMPLE:

x + y=10

5x - y=2

STEP 4: Solve for the other variable use x=2 and x+y=10

x=2 and x+y = 10 therefore:

2+y=10 and y = 8

Solution to the system is (2,8)

GIVEN EXAMPLE:

x + y=10

5x - y=2

Check solution (2,8)

5x-y=2

5(2)-(8)=2

10-8=2

2=2

x + y=10

2+8=10

10=10