Answer:
(x, y) = (2, 4)
Explanation:
You want to solve the system of equations ...
Solution
There are numerous ways to solve this system of equations. One of the simplest is to use a graphing calculator. (See the attachment)
(x, y) = (2, 4)
Substitution
The second equation gives an expression for x that can be substituted into the first equation:
y = -2(y -2) +8
3y = 12 . . . . . . . . add 2y and simplify
y = 4
4-2 = x = 2
The solution is (x, y) = (2, 4).
Elimination
The y-variable has a coefficient of 1 on the left side of the equal sign, so we can eliminate the y-variable by subtracting the second equation from the first.
(y) -(y -2) = (-2x+8) -(x)
2 = -3x +8 . . . . . . . . . . . simplify
3x = 6 . . . . . . . . . . add 3x-2
x = 2 . . . . . . . . divide by 3
y = -2(2) +8 = 4 . . . . . substitute for x in the first equation
The solution is (x, y) = (2, 4).