Nashville Learning Center SAT Tip

Solving Systems of Equations by Elimination (Addition)

Solving Systems of Equations by Elimination (Addition)

To Solve Systems of Equations by Elimination (Addition) you want to eliminate one of your two variables Arrange the equations with like terms in columns.

-2x + 3y =  8
 3x  -   y = -5

Analyze the coefficients of x or y. Multiply one or both equations by an appropriate number to obtain new coefficients that are opposites
In other words you want to work with either your x or your y and you want them to have the same value but one needs to be negative and one positive. So if one y is 4 the other needs to be -4. In our case we will multiply the second equation by 3.

  -2x + 3y =  8
3(3x  -   y = -5) = 9x -3y = -15

Add the equations and solve for the remaining variable.
-2x + 3y =  8
 9x  - 3y = -15

Now add vertically, your y's will cancel out.

-2x + 9x = 7x and 8 + -15 = -7

7x = -7x

Solve for x and you get x = -1

Substitute the value into either equation and solve.

-2(-1) + 3y = 8
2 + 3y = 8

3y= 6
y = 2

Check the solution.
-2(-1) + 3(2) = 8
2 + 6 = 8
8 = 8