Question

How do you solve this set of equations: `2x + 3y = 12; 6x + 9y = 12`?

Answer 1

See a solution process below:

Explanation:

Multiply the first equation by `color(red)(3)`:

`color(red)(3)(2x + 3y) = color(red)(3) * 12`

`(color(red)(3) * 2x) + (color(red)(3) * 3y) = 36`

`6x + 9y = 36`

Because both equations are the same on the left side of the equation but are equal to different constants on the right side of the equation we have the situation where `12 != 36`

Therefore, there is no solution to this problem. Or the solution is the null or empty set: `{O/}`

This indicates the two lines are parallel and not the same line so they never intersect.