Solving Systems of Equations Elimination Method
Solve: 6x + 4y = 8 -x - 4y = 12
Look at the equations and decide which variable you will eliminate using addition or subtraction Solve: 6x + 4y = 8 -x - 4y = 12
6x + 4y = 8 -x - 4y = 12 5x x
= 20 = 4
Now that you have the value for one of the variables, substitute to find the value of the other variable!!!
x
=
4
6x + 4y = 8 -x - 4y = 12 Substitute value for x to find value for y
6(4) + 4y =8 24 + 4y = 8 4y = -16 y = -4
Now that you have a solution, check the values to make sure that they work!!
Solve: 6x + 4y = 8 -x - 4y = 12 (4, -4) Check -4 -4 (-4) ?= 12 -4 + 16 = 12 12 = 12 YES!!
Solve: -2x + 9y = 23 -2x - 8y = -28 Let’s get rid of the “x” terms! How can we make them opposites of each other? If we multiply the top equation by -1, we eliminate the x values!
-1(-2x + 9y = 23) -2x - 8y = -28 +2x - 9y = -23) -2x - 8y = -28 -17y = -51 y=3
Divide both sides by -17
y=3 Solve: -2x + 9y = 23 -2x - 8y = -28 -2x + 9y = 23 -2x + 9(3) = 23 -2x + 27 = 23 -2x = -4 x =2 Solution
(2, 3)
Solution
(2, 3)
-2x + 9y = 23 -2x - 8y = -28 -2x - 8y = -28 -2(2) - 8(3) ?= -28 -4 – 24 ?= -28 -28 = -28
Both sides are equal, so the solution is correct!!