Question

What is the value of the x variable in the solution to the following system of equations?

4x − 3y = 3
5x − 4y = 3

x can be any number as there are infinitely many solutions to this system

There is no x value as there is no solution to this system

−3

3

Answer 1

You just need to solve it like a simultaneous equation. Either multiply the entire top by the y coefficient on the bottom and the bottom by the y coefficient on the bottom or do the same but with the x coefficients. So either multiply the top by 4 and the bottom by 3 or the top by 5 and the bottom by 5. That will give you either x or ys with the same coefficients so you can cancel them out.

So: \[20x - 15y = 15\] and \[20x - 16y = 12\]
In which case, take the bottom from the top and you get 31y = -3 so y = -3/31 then put that back into either of the original equations to get x.

Or do the easier method and cancel the ys to just get x straight away.
So: \[16x - 12y = 12\] and \[15x - 12y = 9\]
So take the bottom from the top and get x = 3
So the answer is x = 3