Solve the system of equations algebraically for real values of x and y
{ x^2 - 11x -y =-24 x^2 -11x +y =-24
Please enter your answer as two ordered pairs in the form (x 1, y 1), (x 2, y 2). The pairs must be separated by a comma.
+23245 Solve for x and y: x2 - 11x - y = -24
x2 - 11x + y = -24
Add down the columns: 2x2 - 22x = -48
Divide by 2: x2 - 11x = -24
Add 24 to both sides: x2 - 11x + 24 = 0
Factor: (x - 8)(x - 3) = 0
Solve: x = 8 or x = 3
Replace x in the first equation: x2 - 11x - y = -24
(8)2 - 11(8) - y = -24 (3)2 - 11(3) - y = -24
64 - 88 - y = -24 9 - 33 - y = -24
-24 - y = -24 -24 - y = -24
-y = 0 -y = 0
y = 0 y = 0
---> (8, 0) ---> (3, 0)
You would have gotten the same y-values had you replaced x in the second equation.
