Question

Solve the system of linear equations below. 2x + 3y = 2 x + 6y = 4

Answer 1

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

To make it more clear.

Answer 2

We will mark equation 1 as E1 and equation 2 as E2
First we will switch E1 with E2
2x + 3y = 2
x + 6y = 4

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

Now will do following E2=E2 - 2*E1

----> x + 6y =4 ----> x + 6y = 4
(2-2)x + (3-2*6)y =2 -2*4 0*x + -9y = -6
Now we will work only in the second equation
-9y =-6
y=6/9 =2/3

We will insert it in 2x + 3y = 2
2x +3 *(2/3) =2
2x +2 =2 /-2
2x=0
x=0
The solution will be (0,2/3)

( Curtsy of Google Because I'm not that smart )

Answer 3

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

as @iambatman said it makes it easy if we write it like this, note if we multiply the second equation by -2 on both sides (which we are allowed to do), we get

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

now notice the 2x on top will cancel with the -2x on bottom if we add the equations

2x+(-2x)+3y+(-12y)=-6 which becomes -9y=-6 so y= 6/9

now plug this into either equation to find x.