# Solving Systems of Linear Equations

### Using the Substitution Method

Substitution Method: A method of solving a system of equations by replacing one variable with an equivalent expression containing the other variable.

Ex: If y=2x+5 and x+3y=7, then x+3(2x+5)=7

*Steps of the Substitution Method*

*Steps of the Substitution Method*

*Start with your two equations*

*Start with your two equations*

*Step 1: Solve for the first variable*

*Step 1: Solve for the first variable*

To solve for the first variable you must substitute one of the variables first. So instead of the problem being 2x+y=15 it will be 2x+3x=15. Afterwards combine like terms and solve for x. Which is 3.

**Step 2: Solve for the second variable**

**Step 2: Solve for the second variable**

To solve for the second variable you must substitute again for the other variable. Instead of the equation being y=3x you replace x with 3 to get y. Which is 9.

**Step 3: Write the solution**

**Step 3: Write the solution**

When writing the solution it is always (x,y). If x=3 and y=9 then the solution will be (3,9).

**Step 4: Check your solution**

**Step 4: Check your solution**

To make sure that your answer is correct, you must plug the solution into your original equations. All the x's will be replaced with 3's and all of the y's will be replaced with 9's. If the solution is correct than the equation will work out.