X-y equals 5 and x squared-y squared equals 5 How do you work this out using simultaneous equations?

Answer 1

0

Answer 2

x - y = 5

x^2 - y^2 = 5

Subtract the first equation from the second equation.

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

(x^2 - y^2) - (x - y) = 0

(x - y)(x + y) - (x - y) = 0

(x - y)(x + y - 1) = 0

x - y = 0 or x + y - 1 = 0

x = y do not satisfy both equations of the system, so x cannot be equal to y. Thus we need to find the values of x and y for which x + y - 1 = 0 is true.

x + y - 1 = 0

x = 1 - y

Substitute 1 - y for x to x - y = 5.

x - y = 5

1 - y - y = 5

- 2y = 4

y = -2

Substitute -2 for y to x = 1 - y

x = 1 - y

x = 1 -(-2)

x = 3

Thus the solution of the system is (3, -2).