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Cerrena [4.2K]
2 years ago
9

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

Mathematics
1 answer:
Aliun [14]2 years ago
6 0

The solution of the system of equation is (-7, -2).

<h2>Given</h2>

The system of the equations;

\rm y^2 + x^2 = 53 \\\\y -x = 5

From equation 1

\rm  y -x=5\\\\y = 5+x

Substitute the value of y in equation 1

\rm y^2+x^2=53\\\\(5+x)^2+x^2=53\\\\25+x^2+10x+x^2=53\\\\2x^2+10x+25-53=0\\\\2 x^2 + 10x - 28 = 0     \\\\Divide \ by \ 2 \ both \ side \ the \ equation\\\\x^2 + 5x - 14 = 0\\\\x^2-7x+2x-14=0\\\\x(x-7) + 2(x-7) =0\\\\(x-7) \ (x+2)=0\\\\x-7=0 \ \ x = 7\\\\x +2 =0 \ \ x=-2

The value of x= 2 is rejected because x = 2 not satisfy the equation.

Substitute 2 for the value of x in equation II

y − x = 5

y – 2 = 5

y = 5 +2

y = 7 (x =2, y =7) … Not included in the options

If x = -7

Substitute the value of x = -7 in the equation

\rm y -x=5\\\\y - (-7)=5\\\\y +7= 5\\\\y = 5-7\\\\y = -2

Hence, the solution of the system of equation is (-7, -2).

To know more about System of Equation click the link given below.

brainly.com/question/1495351

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