We are going to use the Elimination Method.
This is: we are going to add both sides of the equations so our result is an equation with just one variable.
We have that if we add the equations, we will eliminate the x term, then we go ahead:
- 6x + y = 6
6x + 3y =- 12
____________
0x + 4y = -6
because -6x + 6x = 0x, y + 3y = 4y and 6 - 12 = -6
Now, we have an equation for y
0x + 4y = -6
↓
4y = -6
Taking 4 to the right side of the equation:
4y = -6
↓
y = -6/4 = -1.5
Then y = -1.5
Now we find x by replacing y = -1.5 in any of the given equations:
-6x + y = 6
↓
-6x - 1.5 = 6
Taking -1.5 and -6 to the right side of the equation:
-6x - 1.5 = 6
↓ taking -1.5
-6x = 6 + 1.5 = 7.5
-6x = 7.5
↓ taking -6
x = 7.5/(-6) = -1.25
Then x = -1.25
Answer- the solution of the system is x = -1.25 and y = -1.5: (-1.25, -1.5)
