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## Solving Systems of Linear Equations

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**1. **Solving Systems of Linear Equations by using the Addition Method
3.3
SSC 105

**2. **Solving a System of Equations by the Addition Method Write both equations in standard form Ax + By = C.
Clear fractions or decimals (optional).
Multiply one or both equations by a number to create opposite coefficients for one of the variables.
Add the equations from step 3 to eliminate one variable.
Solve for the remaining variable.
Substitute the known value found in step 5 into one of the original equations to solve for the other variable.
Check the ordered pair in both equations.

**3. **ExampleSolve the system by using the addition method. 4x + 5y = 2 3x = 1 4y Step 1: Write both equations in standard form.
4x + 5y = 2
3x + 4y = 1
Step 2: There are no fractions or decimals.

**4. **Example (continued) Solve the system by using the addition method. 4x + 5y = 2 3x = 1 4y Step 3: Multiply the first equation by 3. Multiply the second equation by 4.
4x + 5y = 2 12x + 15y = 6
3x + 4y = 1 12x 16y = 4
Step 4: Add the equations.
12x + 15y = 6
12x 16y = 4
y = 2