Substitution is used to solve systems of equations and to solve real world word problems. It is just one method of solving equations. This method requires replacing a variable with its value. After you replace the variable with it's value you solve the equation.

Method

1. Solve one of the equations for either x or y.

3x + 8y = 80
x + 7y = 18
to
3x + 8y = 80
x = 18 - 7y

2. Replace the variable in the other problem with what you solved for.

3(18 - 7y) + 8y = 80

3. Solve the new equation.

54 - 21y + 8y = 80
54 - 13y = 80
-13y = 26
y = -2

4. Replace the new value in the equation you solved for in step 1 and solve.

x = 18 - 7(-2)
x = 18 + 14
x = 32

x = 32, y = -2

Example 1

Remember:

There must be the same number of equations as there are variables.

One of the equations usually is easier to solve for one variable.

## 7-2 - Substitution

Substitution is used to solve systems of equations and to solve real world word problems. It is just one method of solving equations. This method requires replacing a variable with its value. After you replace the variable with it's value you solve the equation.Method1.Solve one of the equations for eitherxory.x + 7y = 18

to

3x + 8y = 80

x = 18 - 7y

2.Replace the variable in the other problem with what you solved for.3.Solve the new equation.54 - 13y = 80

-13y = 26

y = -2

4.Replace the new value in the equation you solved for in step 1 and solve.x = 18 + 14

x = 32

x = 32, y = -2

Example 1Remember:usuallyis easier to solve for one variable.Examplesregentsprep.org

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