1. Use addition to eliminate a variable
EXAMPLE 1
Use addition to eliminate a variable
Solve the linear system:
2x + 3y = 11
Equation 1
–2x + 5y = 13
Equation 2
SOLUTION
STEP 1
Add the equations to
eliminate one variable.
2x + 3y = 11
–2x + 5y = 13
STEP 2
Solve for y.
8y = 24
y = 3

2. Use addition to eliminate a variable
EXAMPLE 1
Use addition to eliminate a variable
STEP 3
Substitute 3 for y in either equation and
solve for x.
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).

3. Use addition to eliminate a variable
EXAMPLE 1
Use addition to eliminate a variable
CHECK
Substitute 1 for x and 3 for y in each of the original equations.
2x + 3y = 11
2x + 5y = 13
2(1) + 3(3) = 11 ?
2(1) + 5(3) = 13 ?
11 = 11
13 = 13

4. Use subtraction to eliminate a variable
EXAMPLE 2
Use subtraction to eliminate a variable
Solve the linear system:
4x + 3y = 2
Equation 1
5x + 3y = –2
Equation 2
SOLUTION
STEP 1
Subtract the equations to
eliminate one variable.
4x + 3y = 2
5x + 3y = –2
STEP 2
Solve for x.
– x = 4
x = 4

5. Use subtraction to eliminate a variable
EXAMPLE 2
Use subtraction to eliminate a variable
STEP 3
Substitute 4 for x in either equation and solve
for y.
4x + 3y = 2
Write Equation 1.
4(–4) + 3y = 2
Substitute –4 for x.
y = 6
Solve for y.
ANSWER
The solution is (–4, 6).

6. Solve the linear system: 8x – 4y = –4 4y = 3x + 14
EXAMPLE 3
Arrange like terms
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 = –4
8x – 4y = –4
4y = 3x + 14
3x + 4y = 14
STEP 2
Add the equations.
5x = 10
STEP 3
Solve for x.
x = 2

7. Substitute 2 for x in either equation and solve for y.
EXAMPLE 3
Arrange like terms
STEP 4
Substitute 2 for x in either equation and
solve for y.
4y = 3x + 14
Write Equation 2.
4y = 3(2) + 14
Substitute 2 for x.
y = 5
Solve for y.
ANSWER
The solution is (2, 5).

8. GUIDED PRACTICE
for Example 1,2 and 3
Solve the linear system: 1.
4x – 3y = 5 `
–2x + 3y = –7
ANSWER
(–1, –3)

9. GUIDED PRACTICE
for Example 1,2 and 3
Solve the linear system: 2.
5x – 6y = 8 –
5x + 2y = 4
ANSWER
(2, –3)

10. GUIDED PRACTICE
for Example 1,2 and 3
Solve the linear system: 3.
6x – 4y = 14
3x + 4y = 1 –
ANSWER
(5, 4)

11. GUIDED PRACTICE
for Example 1,2 and 3
Solve the linear system: 4.
7x – 2y = 5
7x – 3y = 4
ANSWER
(1, 1)

12. GUIDED PRACTICE
for Example 1,2 and 3
Solve the linear system: 5.
3x + 4y = –6 =
3x + 6 2y
ANSWER
(–2, 0)

13. GUIDED PRACTICE
for Example 1,2 and 3
Solve the linear system: 6.
2x + 5y = 12 =
4x + 6 5y
ANSWER
(1, 2)