1. Multiply one equation, then add
EXAMPLE 1
Multiply one equation, then add
Solve the linear system:
6x + 5y = 19
Equation 1
2x + 3y = 5
Equation 2
SOLUTION
STEP 1
Multiply Equation 2 by –3 so that the coefficients of x are opposites.
6x + 5y = 19
6x + 5y = 19
2x + 3y = 5
–6x – 9y = –15
STEP 2
Add the equations.
–4y = 4

2. Multiply one equation, then add
EXAMPLE 1
Multiply one equation, then add
STEP 3
Solve for y.
y = –1
STEP 4
Substitute –1 for y in either of the original equations and solve for x.
2x + 3y = 5
Write Equation 2.
2x + 3(–1) = 5
Substitute –1 for y.
2x + (–3) = 5
Multiply.
2x = 8
Subtract –3 from each side.
x = 4
Divide each side by 2.

3. Multiply one equation, then add
EXAMPLE 1
Multiply one equation, then add
ANSWER
The solution is (4, –1).
CHECK
Substitute 4 for x and –1 for y in each of the original equations.
Equation 1
Equation 2
6x + 5y = 19
2x + 3y = 5
6(4) + 5(–1) = 19 ?
2(4) + 3(–1) = 5 ?
19 = 19
5 = 5

4. Multiply both equations, then subtract
EXAMPLE 2
Multiply both equations, then subtract
Solve the linear system:
4x + 5y = 35
Equation 1
2y = 3x – 9
Equation 2
SOLUTION
STEP 1
Arrange the equations so that like terms are in columns.
4x + 5y = 35
Write Equation 1.
–3x + 2y = –9
Rewrite Equation 2.

5. EXAMPLE 2
Multiply both equations, then subtract
STEP 2
Multiply Equation 1 by 2 and Equation 2 by 5 so that the coefficient of y in each equation is the least common multiple of 5 and 2, or 10.
4x + 5y = 35
8x + 10y = 70
–3x + 2y = –9
–15x +10y = –45
STEP 3
Subtract: the equations.
23x = 115
STEP 4
Solve: for x.
x = 5

6. Multiply both equations, then subtract
EXAMPLE 2
Multiply both equations, then subtract
STEP 5
Substitute 5 for x in either of the original equations and solve for y.
4x + 5y = 35
Write Equation 1.
4(5) + 5y = 35
Substitute 5 for x.
y = 3
Solve for y.
ANSWER
The solution is (5, 3).

7. Multiply both equations, then subtract
EXAMPLE 2
Multiply both equations, then subtract
CHECK
Substitute 5 for x and 3 for y in each of the original equations.
Equation 1
Equation 2
4x + 5y = 35
2y = 3x – 9
4(5) + 5(3) = 35 ?
2(3) = 3(5) – 9 ?
35 = 35
6 = 6
ANSWER
The solution is (5, 3).

8. GUIDED PRACTICE
for Examples 1 and 2
Solve the linear system using elimination.
6x – 2y = 1 1.
–2x + 3y = –5
ANSWER
The solution is (–0.5, –2).

9. GUIDED PRACTICE
for Examples 1 and 2
Solve the linear system using elimination.
2x + 5y = 3 2.
3x + 10y = –3
ANSWER
The solution is (9, –3).

10. GUIDED PRACTICE
for Examples 1 and 2
Solve the linear system using elimination.
3x – 7y = 5 3.
9y = 5x + 5
ANSWER
The solution is (–10, –5).