Final answer:
To solve the student's question, first solve the two equations for x and y, respectively. Once values are found for x and y, substitute them into the expression x²-(xy-y) to evaluate it. The final answer for the expression, using x=-4 and y=-3, is 1.
Step-by-step explanation:
The question asks to evaluate x²-(xy-y) where x and y satisfy the given equations: x satisfies (4(x+4))/5 = 4x+16 and y satisfies -2y-4 = 7y+23. We first need to solve the equations for x and y before we can substitute their values into the expression x²-(xy-y).
Let's solve for x:
(4(x+4))/5 = 4x+16
Multiply both sides by 5 to eliminate the fraction:
4(x+4) = 20x + 80
Distribute:
4x + 16 = 20x + 80
Now, subtract 4x from both sides:
16 = 16x + 80
Subtract 80 from both sides:
-64 = 16x
Divide both sides by 16:
x = -4
Now let's solve for y:
-2y-4 = 7y+23
Add 2y to both sides:
-4 = 9y + 23
Subtract 23 from both sides:
-27 = 9y
Divide both sides by 9:
y = -3
With x = -4 and y = -3, we can now evaluate the expression x²-(xy-y):
(-4)² - ((-4)(-3) - (-3))
16 - (12 + 3)
16 - 15
The final answer is 1.