# How do you find the solution of the system of equations 14x = 7y + 21 and -18x +9y = 36?

May 8, 2015

In short, there is no solution to this system of equations.

Gather all unknown members on the left side, while putting constants on the right.
$14 x - 7 y = 21$
$18 x - 9 y = - 36$

Simplify both equations by factoring out $7$ in one and $9$ in another:
$2 x - y = 3$
$2 x - y = - 4$

The fact that this system contains the same expression on the left in its two equations and different values for a constant on the right signifies that the system has no solutions. There is no such pair of numbers $\left(x , y\right)$ that would satisfy both equations.