Question

How do you solve the system of equations `12x + 3y = 0` and `-48x - 12y = 0`?

Answer 1

See a solution process below:

Explanation:

If we multiply both sides of the first equation by `color(red)(-4)` which will keep the equation balanced we get:

`color(red)(-4)(12x + 3y) = color(red)(-4) xx 0`

`(color(red)(-4) xx 12x) + (color(red)(-4) xx 3y) = 0`

`-48x + (-12y) = 0`

`-48x - 12y = 0`

This is the same as the second equation. Therefore, the two equations represent the same line which means there are infinite solutions to this problem. For every point `(x, y)` in the first equation it is equal for the second equation.