Do Now Pass out calculators. Solve the following system by graphing: Graph paper is in the back. 5x + 2y = 9 x + y = -3 Solve the following system by using.

Do Now• Pass out calculators. • Solve the following system by graphing: Graph paper is in the back.

5x + 2y = 9 x + y = -3 • Solve the following system by using substitution:

11x – 7y = - 14 x – 2y = -4

Objective:

• To solve systems of equations using elimination (adding or subtracting).

Use addition to eliminate a variable

EXAMPLE 1

Solve the linear system:

2x + 3y = 11 –2x + 5y = 13

Equation 1

Equation 2

SOLUTION

Add the equations toeliminate one variable.

2x + 3y = 11–2x + 5y = 13

Solve for y. 8y = 24y = 3

STEP 1

STEP 2

Use addition to eliminate a variable

EXAMPLE 1

2x + 3y = 11 Write Equation 1

2x + 3(3) = 11 Substitute 3 for y.

x = 1 Solve for x.

ANSWER

The solution is (1, 3).

Substitute 3 for y in either equation and solve for x.

STEP 3

Use addition to eliminate a variable

EXAMPLE 1

2x + 3y = 11

11 = 11

Substitute 1 for x and 3 for y in each of the original equations.

CHECK

2(1) + 3(3) = 11?

2x + 5y = 13

13 = 13

2(1) + 5(3) = 13?

Use subtraction to eliminate a variable

EXAMPLE 2

Solve the linear system:4x + 3y = 2 Equation 1

5x + 3y = –2 Equation 2

SOLUTION

Subtract the equations toeliminate one variable.

4x + 3y = 25x + 3y = –2

Solve for x. – x = 4

STEP 1

STEP 2 x = 4

Use subtraction to eliminate a variable

EXAMPLE 2

4x + 3y = 2 Write Equation 1.

4(–4) + 3y = 2 Substitute –4 for x.

y = 6 Solve for y.

ANSWERThe solution is (–4, 6).

Substitute 4 for x in either equation and solvefor y.

STEP 3

Arrange like terms

EXAMPLE 3

Solve the linear system:8x – 4y = –4 Equation 1

4y = 3x + 14 Equation 2

SOLUTION

STEP 1 Rewrite Equation 2 so that the like terms are arranged in columns.8x – 4y = –44y = 3x + 14

8x – 4y = –43x + 4y = 14

STEP 2 Add the equations. 5x = 10

STEP 3 Solve for x. x = 2

Arrange like terms

EXAMPLE 3

4y = 3x + 14 Write Equation 2.

4y = 3(2) + 14 Substitute 2 for x.

y = 5 Solve for y.

ANSWERThe solution is (2, 5).

STEP 4 Substitute 2 for x in either equation and solve for y.

GUIDED PRACTICE for Example 1,2 and 3

Solve the linear system:

4x – 3y = 5 –2x + 3y = –7

`

1.

ANSWER (–1, –3)

GUIDED PRACTICE for Example 1,2 and 3

Solve the linear system:

5x + 2y = 45x – 6y = 8–2.

ANSWER (2, –3)

GUIDED PRACTICE for Example 1,2 and 3

Solve the linear system:6x – 4y = 143x + 4y = 1–

3.

ANSWER (5, 4)

GUIDED PRACTICE for Example 1,2 and 3

Solve the linear system:7x – 2y = 57x – 3y = 4

4.

ANSWER (1, 1)

GUIDED PRACTICE for Example 1,2 and 3

Solve the linear system:

3x + 4y = –65. = 3x + 62y

ANSWER (–2, 0)

GUIDED PRACTICE for Example 1,2 and 3

Solve the linear system:

2x + 5y = 126. = 4x + 65y

ANSWER (1, 2)