We are asked to solve the following system of equations via the addition method:
x + 2 y = - 2
6 x + 3 y = - 30
so via the addition method we will try to eliminate one of the variables by multiplying for the appropriate factor that would ease tha process. We notice that if wemultiply the whole first eqaution by the factor (-6), we will be able to in the second step eliminate the term in "x" by combining both equations term by term.
So we do that: Multiply the whole first equation by "-6":
(-6) (x + 2 y ) = (-6) (-2)
- 6 x - 12 y = 12
now we combine this with the second equation term by term to eliminate the term in x:
- 6 x - 12 y = 12
+
6 x + 3 y = - 30
_______________
0 - 9 y = - 18
Now divide both sides by "-9" to isolate y:
y = - 18 / (-9)
y = 2
Now we use y = 2 in the very first equation to solve for the variable x:
x + 2 y = - 2
x + 2 (2) = -2
x + 4 = - 2
subtract 4 from both sides:
x = - 2 - 4
x = - 6
