Question

How do you solve the system of equations `-6x-10y=20` and `3x+5y=25`?

Answer 1

no solutions - lines are parallel

Explanation:

`-6x - 10y = 20`
`3x + 5y = 25`

multiply all values in the first equation by `-1`, and in the second by `2`:

`6x + 10y = -20`
`6x + 10y = 50`

since `-20` and `50` are distinct integers, they cannot both be solutions to the same (linear) equation.

on a graph:

(`-6x-10y=20` is in red, and `3x+5y=25` is in blue.)

these lines are parallel, meaning that there are no points of intersection between them, and therefore no solutions for this simultaneous equation.

it can be shown that they are parallel by converting both equations to `y=mx+c` form:

`-6x - 10y = 20 -> -10y = 20+6x -> y = -2 - 0.6x`

`3x + 5y = 25 -> 5y = 25 - 3x -> y = 5 - 0.6x`

since the number before `x` is the same in both equations, the lines have the same gradient, and are therefore parallel.