Which two points satisfy y=-x2(^)+2x+4 and x+y=4? a. (0,4) and (4,0) b. (0,4) and (3,1) c. (7,-3) and (0,4) d. (7,-3) and (4,0)

Use subtitution method to solve the problem.

First, change y to the value of x in order to find the exact value of x.
x + y = 4
y = 4 - x

Second, subtitute y with 4 - x from the first equation
y = -x² + 2x + 4
4 - x = -x² + 2x + 4
move all terms to the left side
x² - 2x - x + 4 - 4 = 0
x² - 3x = 0
x(x - 3) = 0
x = 0 or x = 3

Third, now we have 2 values of x. Find the value of y for each of x
For x = 0
y = 4 - x
y = 4 - 0
y = 4

For x = 3
y = 4 - x
y = 4 - 3
y = 1

The solution is (0,4) and (3,1). The answer is option b