What is one of the solutions to the following system of equations? y2 + x2 = 53. y − x = 5. a. (−10, −5) b. (−7, −2) c. (7, 2) d. (5, 10)

Answer is (-7, -2)

Rewrite the equations so that both are set equal to 0: 
y^2 + x^2 = 53
y^2 + x^2 - 53 = 0

y - x = 5 
y - x - 5 = 0 

Set them equal to eachother: 
y^2 + x^2 - 53 = y - x - 5
y^2 + x^2 = y - x + 48
Plug in the value options and see which one works. 
A) (-10, -5)
25 + 100 = -5 + 10 + 48      Does not work, eliminate option

B) (-7,-2) 
4 + 49 = -2 + 7 + 48
53 = 53                                We have a match!
We can stop checking now, we've found the coordinate pair that solves. 

Answer is B) (-7, -2)

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