Solve Remember that graphs can be used to confirm all real s

Solve. Remember that graphs can be used to confirm all real solutions 2x-y E 1 One solution of the system is 3 3 The other solution is (Type an ordered pair.)

Solution

y^2 - x^2 = 5

2x -y = 1

substitute y = 1 -2x in equation1:

(1- 2x)^2 - x^2 =5

1 +4x^2 - 4x -x^2 =5

3x^2 -4x -4 =0

solev by factorisation :

3x^2 -6x +2x -4 =0

3x( x-2) +2(x-2) =0

(3x +2)(x-2)

x = -2/3 ; x=2

y = 1-2x = 1 +4/3

y = 7/3

y = 1 -2*2 = -3

Solution ( -2/3 , 7/3) and ( 2 ,-3)