two systems of equations are given below for each system, choose the best description of it solution.

Question

1) the system has no solution
2) the system has a unique solution
3) the system has a infinitity many solutions. they must satisfy the following equation

x+4y=8
-x-4y=-8

-x-2y=4
x+2y=4

Answer 1

If you add the first two equations, you will get 0 = 0

Any time you have a situation when the variables disappear and you end up with a true statement, there are an infinite number of solutions. Whatever (x,y) works in one equation will also work in the other.

The second set adds to 0 = 8
This is false which means there are no solutions. You cannot find an (x,y) that will work in both equations.