07-2+Substitution



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__ **
x + 7y = 18 to 3x + 8y = 80 x = 18 - 7y || 54 - 13y = 80 -13y = 26 y = -2 || x = 18 + 14 x = 32
 * **1.** Solve one of the equations for either //x// or //y//. || 3x + 8y = 80
 * < **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
 * **4.** Replace the new value in the equation you solved for in step 1 and solve. || x = 18 - 7(-2)

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.

__Examples__



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