Question

Using the linear combination method, find the solution to this system of equations. Be sure to show all your steps in your work!

5x+4y=-14

3x+6y=6

Answer 1

`x=-6; y=4`

Explanation:

Step 0: retwite the second equation by dividing LHS and RHS by 3.

`x+2y=2`

Step 1: combine them as the first minus twice the second to eliminate y

`I - 2* II : 5x+4y -2x-4y=-14-4 \rightarrow 3x=-18 \rightarrow x= -6`

Step 2a: At this point I would replace the value of x in the second equation to easily solve for y. That will give you
`-6+2y=2 \rightarrow y=4`. I do imagine you're required to use the same method to solve for y even if it's slower so...

Step 2b: Combine them again, taking the first minus 5 times the second to eliminate x:

`I-5II: 5x+4y-5x-10y=-14-10 \rightarrow -6y=-24 \rightarrow y=4`