How do you find the solution of the system of equations #y= x^2 + 5# and # y = 2x + 4#?

1 Answer
May 9, 2015

Since you have already been given two expressions for #y#, why not combine them to eliminate #y# and solve for #x#?

#x^2 + 5 = 2x + 4#

Subtract #2x + 4# from both sides to give the quadratic:
#x^2 - 2x + 1 = 0#

You don't need to use the general quadratic solution to simply notice that #0 = x^2 - 2x + 1 = (x - 1)(x - 1)#.

So there's just one (repeated) solution with #x = 1#.

Substitute #x = 1# into either of the original equations to get #y = 6#.