What is one of the solutions to the following equations? y2+x2=53
Y-x=5
1 answer:
(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 = 3Answer: x = 2 and y = 7 or x = -7 and y = 3
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