How do you solve 8x-6y=14 and 12x-9y=18?

Apr 26, 2018

This is an inconsistent system, with no solutions.

Explanation:

Given:

$\left\{\begin{matrix}8 x - 6 y = 14 \\ 12 x - 9 y = 18\end{matrix}\right.$

Note that all of the coefficients of the first equation are divisible by $2$ and all of the coefficients of the second equation are divisible by $3$. So divide the first equation by $2$ and the second by $3$ to get:

$\left\{\begin{matrix}4 x - 3 y = 7 \\ 4 x - 3 y = 6\end{matrix}\right.$

So any solution to this system must satisfy:

$7 = 4 x - 3 y = 6$

which is false.

This is an inconsistent system with empty solution space.

If we graph the two lines represented by the system, we find that they are parallel, with no point of intersection...

graph{(4x-3y-7)(4x-3y-6) = 0 [-4.813, 5.187, -2.66, 2.34]}