Which ordered pair is the solution to the system of equations #y=x# and #y=x^2-2#?

1 Answer
Aug 24, 2016

Answer:

#(x, y) = (2, 2) " "# or #" " (x, y) = (-1, -1)#

Explanation:

If the first equation is satisfied then we can replace #y# with #x# in the second equation to get:

#x = x^2-2#

Subtract #x# from both sides to get the quadratic:

#0 = x^2-x-2 = (x-2)(x+1)#

Hence solutions #x=2# and #x=-1#.

To make each of these into ordered pair soltuions of the original system, use the first equation again to note that #y = x#.

So the ordered pair solutions to the original system are:

#(2, 2) " "# and #" " (-1, -1)#