Question

X2 + y2 = 13

x2 - y2 = 5
Check all of the following that are solutions to the system shown.

A. (3, 2)
B. (3, -2)
C. (-3, 2)
D. (-3, -2)

Answer 1

All are corect.

Answer 2

(3,2),(3,-2),(-3,2),(-3,-2)

Explanation:

The given system of equations is

`x^2+y^2=13...(i)\\\\x^2-y^2=5...(ii)`

Add equations (i) and (ii) is

`2x^2=18`

Solve the equation for x. For this divide both sides by 2

`x^2=9`

Take square root both sides

`√(x^2)=\pm\sqrt9\\\\x=\pm3`

For x = 3, -3

`(\pm3)^2+y^2=13\\9+y^2=13\\y^2=4\\y=\pm2`

Therefore, the solutions are

(3,2),(3,-2),(-3,2),(-3,-2)

Therefore, all the points are the solutions of the system of equations.