## Elementary Algebra

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: $x = \frac{ b_1c_2 - b_2c_1}{a_2b_1 - a_1b_2}$