Answer
The answer is below.
Work Step by Step
We first isolate x in both equations:
For equation one:
$ a_1 x = c_1 - b_1y \\ x = \frac{c_1 - b_1y}{a_1}$
Doing the same thing for equation two yields:
$ x = \frac{c_2 - b_2y}{a_2}$
Combining these and cross multiplying gives:
$a_2c_1 - a_2b_1y =a_1c_2 - a_1b_2y \\ $
Solving for y gives:
$ y = \frac{a_2c_1 - a_1c_2}{a_2b_1 - a_1b_2}$
Plugging this in for y and simplifying gives an x value of:
$x = \frac{ b_1c_2 - b_2c_1}{a_2b_1 - a_1b_2}$
