Question

What is one of the solutions to the following system of equations?

y2 + x2 = 53
y − x = 5

Answer 1

x = 2 and y = 7

Explanation:

The given equations are :

`y^2+x^2=53\ ....(1)\\\\y-x=5\ ...(2)`

Squaring both sides of equation (2)

`(y-x)^2=5^2\\\\y^2+x^2-2xy=25\\\\53-2xy=25\ \text{from equation (1)}\\\\2xy=53-25\\\\2xy=28\\\\xy=14\ ...(3)`

Put the value of y from equation (2)

`x(5+x)=14\\\\5x+x^2-14=0\\\\x=2`

Put the value of x in equation (2)

y-x = 5

y = 5+x

= 5+2

= 7

Hence, the solution of the given equations are (2,7).