Equation 3

Problem:

2x=-y+6
-4x+3y=8

Solution:

The way to solve these equation is trying to eliminate variable by subtracting them away. In this one, we see 2x and -4x, so a natural way to eliminating it is multiply the first equation by 2 and then sum them together.

$ 4x = -2y + 12 $ [This come from the first equation multiplied by 2]
$ -4x + 3y = 8 $ [This is just the second equation]

Sum the left and right side, we get


$ 3y = -2y + 12 + 8 $

Now it becomes a trivial equation to solve, we get $ y = 4 $

Now you can solve $ x $ however you want since you already $ y $, the easiest way is to put it back to the first equation, we get $ 2x = -4 + 6 $, in which we get $ x = 1 $.