1. Use the substitution method
EXAMPLE 1
Use the substitution method
Solve the system using the substitution method.
2x + 5y = –5
Equation 1
x + 3y = 3
Equation 2
SOLUTION
STEP 1
Solve Equation 2 for x.
x = –3y + 3
Revised Equation 2

2. Use the substitution method
EXAMPLE 1
Use the substitution method
STEP 2
Substitute the expression for x into Equation 1 and solve for y.
2x +5y = –5
Write Equation 1.
2(–3y + 3) + 5y = –5
Substitute –3y + 3 for x.
y = 11
Solve for y.
STEP 3
Substitute the value of y into revised Equation 2 and solve for x.
x = –3y + 3
Write revised Equation 2.
x = –3(11) + 3
Substitute 11 for y.
x = –30
Simplify.

3. Use the substitution method
EXAMPLE 1
Use the substitution method
The solution is (– 30, 11).
ANSWER
CHECK Check the solution by substituting into the original equations.
2(–30) + 5(11) –5 = ?
Substitute for x and y. = ?
–30 + 3(11) 3
–5 = –5
Solution checks.
3 = 3

4. Use the elimination method
EXAMPLE 2
Use the elimination method
Solve the system using the elimination method.
3x – 7y = 10
Equation 1
6x – 8y = 8
Equation 2
SOLUTION
STEP 1
Multiply Equation 1 by – 2 so that the coefficients of x differ only in sign.
3x – 7y = 10
–6x + 14y = 220
6x – 8y = 8
6x – 8y = 8

5. Use the elimination method
EXAMPLE 2
Use the elimination method
STEP 2
Add the revised equations and solve for y.
6y = –12
y = –2
STEP 3
Substitute the value of y into one of the original equations. Solve for x.
3x – 7y = 10
Write Equation 1.
3x – 7(–2) = 10
Substitute –2 for y.
3x + 14 = 10
Simplify.
x = 4 3 –
Solve for x.

6. EXAMPLE 2
Use the elimination method
The solution is ( , –2) 4 3 –
ANSWER
CHECK
You can check the solution algebraically using the method shown in Example 1. You can also use a graphing calculator to check the solution.

7. GUIDED PRACTICE
for Examples 1 and 2
Solve the system using the substitution or the elimination method. 1.
4x + 3y = –2
x + 5y = –9 2.
3x + 3y = –15
5x – 9y = 3
The solution is (1,–2).
ANSWER
The solution is ( , –2) 3 –
ANSWER

8. GUIDED PRACTICE
for Examples 1 and 2
Solve the system using the substitution or the elimination method. 3.
3x – 6y = 9
–4x + 7y = –16
ANSWER
The solution is (11, 4)