Question

Solving Quadratic System

x^2+4y^2=16
x^2+y^2=4

Please SHOW WORK I'm having trouble solve this...

Answer 1

x ^ 2 + 4 y ^ 2 = 16

- x ^ 2 + y ^ 2 = 4
______________________

3 y ^ 2 = 12 Divide both sides by 3

y ^ 2 = 12 / 3 = 4

y = + OR - 2

For y = 2

x ^ 2 + 4 y ^ 2 = 16

x ^ 2 + 4 * 2 ^ 2 = 16

x ^ 2 + 4 * 4 = 16

x ^ 2 + 16 = 16 Subtract 16 to both sides

x ^ 2 = 0

x = 0

For y = - 2

x ^ 2 + 4 y ^ 2 = 16

x ^ 2 + 4 * (- 2 ^ 2 ) = 16

x ^ 2 + 4 * 4 = 16

x ^ 2 + 16 = 16 Subtract 16 to both sides

x ^ 2 = 0

x = 0

The solutions are :

x = 0 , y = 2

( 0 , 2 )

and

x = 0 , y = - 2

( 0 , - 2 )