Question

how do i use elimination to solve 2x+3y=1
4x-5y=13

Answer 1

Actual matrix algebra or just the good old substitute and solve method?

Answer 2

If you don't need to set it up as a matrix, just solve for one variable in terms of the other and substitute it into the other equation and solve it.

So x = (13-5y) / 4 from the second equation. Substitute that into the first equation where you see the x, solve it for the only remaining variable, y, and then substitute that value you found for y back into the equation (either equation) and solve for x.