Answer:
(8, -1)
Explanation:
We will use substitution to solve this. First we will isolate y in the second equation:
y+x = 7
Subtract x from each side:
y+x-x = 7-x
y = 7-x
Substitute this in place of y in the first equation:
(7-x)²+x² = 65
(7-x)(7-x)+x² = 65
7(7)-7(x)-x(7)-x(-x) + x² = 65
49-7x-7x+x²+x² = 65
Combining like terms,
49-14x+2x² = 65
Writing in standard form,
2x²-14x+49 = 65
Subtracting 65 from each side,
2x²-14x+49-65 = 65-65
2x²-14x-16 = 0
We can factor 2 out of this:
2(x²-7x-8) = 0
To factor the remaining trinomial, find factors of -8 that sum to -7. -8 and 1 work:
2(x-8)(x+1) = 0
Using the zero product property, x-8 = 0 or x+1 = 0. This gives us x = 8 or x = -1.
Substituting these into the second equation,
y+8 = 7 or y-1 = 7
y = -1 or y = 8
This gives us the point (8, -1).