Solving Systems of Equations Algebraically - PowerPoint Presentation

Slide1

Solving Systems of Equations Algebraically

Substitution and EliminationSlide2

Elimination

Arrange the equations in STANDARD FORM.

Your goal is to find a way to eliminate one of the variables so you can solve a one-variable equation.

+ ( )

2x

+ 0

= 12

2x = 12

2 2

x = 6

x + y = 10

6

+ y = 10

-6 -6

y = 4

Now substitute your answer for x into one of the original equations and solve for the y answer.

Sometimes adding the two equations together will eliminate one of the variables.

(6, 4)Slide3

Elimination

Sometimes you need to subtract the equations so you can eliminate a variable.

-

( )

0 - 2y = -4

-2y = -4

-2 -2

y = 2

Substitute your

y

value back into either one of the original equations.

x + y = 7

x +(2) = 7

-

2

-

2

x = 5

(5, 2)Slide4

Elimination

Sometimes you need to alter one or both of the equations so you can eliminate a variable.

2( )

+

( )

7x + 0 = 28

7x = 28

7

7

x = 4

x + 2y = 10

4

+ 2y = 10

-4 -4

2y = 6

2

2

y = 3

(4, 3)Slide5

Substitution

You can isolate a variable and use what it equals in the other equation.

y

= (x + 1)

2x +

(

y

) = 72x + (

x + 1) = 7

3x + 1 = 7Solve

3x = 6

-1 -1

3

3

x = 2

I

solate

Replace y

With (x + 1)

Simplify

y

= x + 1

Now substitute

y

=

2

+ 1

y

=

3

(2, 3)Slide6

Substitution

Solve

I

solate

Replace x

Simplify

Now substitute

4x = 8y

4

4

2x + 5y = 27

x = 2y

2(

2y

) + 5y = 27

4y + 5y = 27

9y = 27

9

9

y = 3

4x = 8y

4x = 8(3)

4x = 24

4

4

x = 6

(6, 3)