Question

What is one of the solutions to the following system of equations?

y2 + x2 = 65
y + x = 7

Answer 1

From the second equation, y = 7 - x

So substitute 7 - x into x in the first equation...now work that out.

Answer 2

(7 - x)^2 + x^2 = 65

Answer 3

49 - 14x + x^2 + x^2 = 65

Answer 4

2x^2 - 14x + 49 = 65

Answer 5

2x^2 - 14x - 16 = 0

Answer 6

2x^2-14x==16

Answer 7

Factor out a 2: 2(x^2 - 7x - 8) = 0
x^2 - 7x - 8 = 0
(x - 8)(x + 1) = 0
x = 8 and x = -1

If x = 8, y = -1
If x = -1, then y = 8

Pairs of solutions are (8,-1) and (-1,8)

Answer 8

(−8, 1)

(1, 6)

(6, 1)

(9, −2)