Answer:
I'm not sure if there's a typo so I did both
When y = x^2 - 7 + 12: x=5 or x=1 , y = 6 or 30
When y = x^2 -7x + 12: x = 12 or x = 1, y = 72 or 6
Step-by-step explanation for y = x^2 -7 + 12:
Simplify
y=6x
y = x^2+5
Substitute y = 6x into the quadratic
6x = x^2+5
Make the quadratic equate to 0
6x = x^2+5
-6x -6x
0 = x^2 - 6x + 5
Factor
What multiplies to c and adds to b?
(x-5)(x-1) = 0
Solve for small equations
x-5 = 0 x-1 = 0
+5 +5 +1 +1
x=5 or x=1
Substitute to find y
y = 6 (5 or 1)
y = 6 or 30
Step-by-step explanation for y = x^2 -7x + 12:
Equate y to 6x
6x = x^2 - 7x + 12
Equate to 0
6x = x^2 - 7x + 12
-6x -6x
0 = x^2 - 13x + 12
Factor
What multiplies to c and adds to b?
(x - 12)(x - 1)
Solve for x
x-12 = 0 x-1 = 0
+12 +12 +1 +1
x = 12 or x = 1
Substitute for x to find y
y = 6(12 or 1)
y = 72 or 6
