Question

2x − 4y = 36 −x + 2y = −18 ( x,y) =

Answer 1

In this system of equations, x and y have an infinite number of solutions.

We can see this when we try to solve, either by elimination or by substitution.
For substitution, we can take the equation -x + 2y = -18 and rearrange to get x = 2y + 18.
Then we can substitute this into the first equation:

2(2y + 18) - 4y = 36
4y + 36 - 4y = 36
36 = 36
which gives us no solutions.

For elimination, we can multiple the second equation by -2 so that the y coefficient is also -4:
-2(-x + 2y) = -2(-18)
2x - 4y = 36
which just gives us the first equation.

Therefore, we can deduce that any solution that would work for one equation will work for the other equation, so there are an infinite number of solutions.

I hope this helps! Let me know if you have any questions :)