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

May 9, 2015

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

${x}^{2} + 5 = 2 x + 4$

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

You don't need to use the general quadratic solution to simply notice that $0 = {x}^{2} - 2 x + 1 = \left(x - 1\right) \left(x - 1\right)$.

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

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