Question

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

Answer 1

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.
`14x-7y=21`
`18x-9y=-36`

Simplify both equations by factoring out `7` in one and `9` in another:
`2x-y=3`
`2x-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 `(x,y)` that would satisfy both equations.