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
We can use substitution to find a solution. We substitute the expression for y from the second equation into the first equation:
y = 6 - x
x - 2 = 6 - x
Adding x to both sides and adding 2 to both sides, we get:
2x = 8
So x = 4. Now we can use either equation to find y. Using y = x - 2, we get:
y = 4 - 2 = 2
So the solution is (4, 2).
Therefore, the answer is C. (4, 2).