Question

Find the solution of this system of equations

8x - 2y = -54

2x - 2y = 0

Answer 1

x = -9

y = -9

Explanation:

We notice that the two equations shared an identical term in their standard form, the term "-2y". Therefore, this term can be easily cancelled out by combining the two equations. We subtract the two equations term by term so as to remove the term in the variable "y" which will leave us with an equation containing only the unknown "x" for which we can solve:

`8x-2y=-54\\-\\2x-2y=0\\8x-(2x)-2y-(-2y)=-54-0\\6x=-54\\x=(-54)/(6) \\x=-9`

Now, we use this found value for "x" in either of the original equations, for example in 2x - 2y = 0 to solve for the variable "y":

`2x-2y=0\\2(-9)-2y=0\\-18-2y=0\\-18=2y\\y=(-18)/(2) \\y=-9`

So the solution to this set is the pair x = -9 and y = -9

(-9, -9)