Find the solution to the system of equations by using either graphing or substitution.
y=6-x and y=x-2
A) (2,4)
B) (-4,2)
C) (4,2)
D) no solutions
To solve this system of equations, we can use substitution.
y = 6 - x
y = x - 2
First, set the two equations equal to each other:
6 - x = x - 2
Add x to both sides:
6 = 2x - 2
Add 2 to both sides:
8 = 2x
Divide by 2:
x = 4
Now plug x = 4 back into one of the original equations to solve for y. We'll use y = 6 - x:
y = 6 - 4
y = 2
Therefore, the solution to the system of equations is (4, 2), which corresponds to answer choice C.