Question

What is one of the solutions to the following equations? y2+x2=53 Y-x=5

Answer 1

(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