# How do you solve y = x² and 1 + y = 2x using substitution?

May 3, 2016

We already know the value of y, so it's just a matter of substituting.

#### Explanation:

$y = {x}^{2} \to 1 + {x}^{2} = 2 x$

${x}^{2} - 2 x + 1 = 0$

$\left(x - 1\right) \left(x - 1\right) = 0$

$x = 1$

$y = {x}^{2}$

$y = {\left(1\right)}^{2}$

$y = 1$

The solution set is $\left\{1 , 1\right\}$

Hopefully this helps!