System of equations
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.
Step 1
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
Step 2
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
Step 3
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)