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.

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
math_problems.jpg

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.

Examples




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