What is one of the solutions to the following equations? y2+x2=53

Y-x=5

(1) y² + x² = 53

(2) y - x = 5 ⇒ y = x + 5

subtitute (2) to (1)

(x + 5) ² + x² = 53 |use (a + b) ² = a² + 2ab + b²

x² + 2x·5 + 5² + x² = 53

2x² + 10x + 25 = 53 |subtract 53 from both sides

2x² + 10x - 28 = 0 |divide both sides by 2

x² + 5x - 14 = 0

x² - 2x + 7x - 14 = 0

x (x - 2) + 7 (x - 2) = 0

(x - 2) (x + 7) = 0 ⇔ x - 2 = 0 or x + 7 = 0 ⇔ x = 2 or x = - 7

subtitute the values of y to (2)

for x = 2, y = 5 + 2 = 7

for x = - 7, y = 5 + (-7) = 5 - 2 = 3

Answer: x = 2 and y = 7 or x = - 7 and y = 3