Question

Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite.
x + y = 4
x - y = 0

A.{}
B.1 solution
C.infinite

Answer 1

well you are looking for 2 numbers, x and y

when you add x and y, you want it to equal 4
when you subtract x and y, you want it to equal 0

Answer 2

in essence this means that x and y must be equal to each other.

simply because x - y = 0 is only true when x = y

Answer 3

therefore, all you need to find is 2 numbers when added together equal 4

the only possible solution is the number 2, as 2 +2 = 4 and 2 - 2 = 0

does that make sense?

Answer 4

you could solve it algebraically also

x + y = 4
x - y = 0
add both equations
2x = 4
x = 2

since x = y, then y also = 2. therefore there is 1 solution (2,2)