FX-36 Elimination Method

Melanie Thomas

5x-4y=7
2y+6x=22

To use the elimination method to solve this system of linear equations, first you have to eliminate y, to find x.

To do this, you have to add its additive inverse.
First, multiply both sides of the second equation by 2 in order to get 4y so that the -4y from the first equation cancels out when added to the 4y from the second equation.

2(2y+6x)=22(2)
4y+12x=44

Once you've done this, in order to solve the system, add 4y+12x to the left side of the first equation and then add 44 to the right side of that same equation. Now the equations are in standard form but the coefficients and variables need to be lined up. The system of equations should now look like this:
5x-4y=7
12x+4y=44
-----------------
17x+0y=51

Once you've done this you should get 17x=51 because 5x+12x=17x, the -4y+4y cancel out and you're left with 0y, and 7+44=51. After this, you solve for x.

To solve for x, you divide both sides of the equation by 17:
17x/17=51/17
x=3

On the left side, you're left with an isolated x variable and on the right side you're left with 3 because 51/17=3.

Now you have to solve for y, and to do this, the first step would be to substitute 3 for x in either of the original equations. In the first equation:

5x-4y=7, it would be
5(3)-4y=7 then you'd simplify and it would be:
15-4y=7
After this, you subtract 15 from both sides to isolate the 4y, which is the second step of solving for y.

15-4y=7
-15 -15
-----------------
-4y= -8


You're left with -4y=-8 and to isolate y, you divide both sides by -4.

-4y/-4 =-8/-4

y=2

You're left with 2.

Now use the numbers that were found for the x and y variables and the solution of the system is (3, 2).