sole the systems of equations algebraically.

Question

find all solutions y^2-x^2=12 and x^2+y^2=20

Answer 1

Elimination method

Given systems y ^2 - x ^2 = 12 ---> (1)

x ^2 + y ^2 = 20

y ^2 + x ^2 = 20 ---> (2)

To eliminate the x ^2 value add the equations (1) and (2).

y ^2 - x ^2 = 12

y ^2 + x ^2 = 20

___________________

2y ^2 = 32

y ^2 = 32/2

y ^2 = 16

Substitute the  y ^2 value in equation (2 ).

16 + x ^2 = 20

x ^2 = 20 - 16

x ^2 = 4.

Now x ^2 = 4

Apply squre root on each side.

x = ± 2

Now y ^2 = 16

Apply squre root on each side.

y = ± 4

Solutions x = +2,-2 and y  = +4,-4.