What is one of the solutions to the following system of equations? y2 + x2 = 65 y + x = 7 (2 points) (8, -1) (1, 6) (6, 1) (9, -2)

(8, -1)

Step-by-step 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).

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step-by-step explanation: