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Solving Systems of Equations by Graphing

Name: Pd

Algebra 2/26/09

System of Linear

Equations: y = 2/5x – 2 y = -3x + 15{

Solution to a System of Linear Equations:

Solution (5, 0)

2/5(5) – 2 = 0 -3(5) + 15 = 0{

x, y

having more than one linear equation.

is the ordered pair or pairs that satisfy all equations.

Three ways to solve a system of equations:

Graphing

Elimination

Substitution

y = 2/5x – 2 y = -3x + 15{

5x + 3y = 3 2x – y = 6 {

4x – 3y = 6 y = -3x + 15{

There are three possible outcomes for the solutionsof a system:

One Solution

No Solution

Infinite Solutions

(1, 1)

(0, -3)

(-1, 2) (1, 4)

Ex1: Find the solution to the given system by graphing.

y = -1x + 3y = 1/2x – 3{

Solution: (4, -1)

y = 2x – 5y = -3/2x + 2{

Solution: (2, -1)

Ex2: Find the solution to the given system by graphing.

y = -5y = -4x + 3{

Solution: (2, -5)

Ex3: Find the solution to the given system by graphing.

y = -1/2x + 3y = -1/2x – 1 {

No Solution

Ex4: Find the solution to the given system by graphing.

Ex5: Find the solution to the systems by graphing.

2x + 6y = -12 4x – 4y = -8 {

2x + 6y = -12-2x -2x

6y = -12 – 2x 6 6y = -2 –1/3x

4x – 4y = -8 -4x -4x

-4y = -8 – 4x -4 -4

y = 2 + x

Solution (-3, -1)

Ex6: Find the solution to the systems by graphing.

-4x + 8y = 16 6x – 3y = 12{

-4x + 8y = 16+4x +4x

8y = 16 + 4x 8 8y = 2 + 1/2x

6x – 3y = 12 -4x -6x

-3y = 12 – 6x -3 -3

y = -4 + 2x

Solution (4, 4)

Ex7: Find the solution to the systems by graphing.

{

x – y = 4 -1x -1x

-1y =-1x + 4 -1 -1 -1y = 1x – 4

-5x + 5y = -20 +5x +5x

5y = 5x – 20 5 5 5

y = 1x – 4

Infinite Solutions

x – y = 4 -5x + 5y = -20

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• Tomorrow we will continue with solving systems of equations by graphing.