# How do you solve the system y = x² and 1 + y = 2x?

Mar 9, 2016

$x = 1 , y = 1$

#### Explanation:

When trying to find values of x and y in a system, check first which value can be easily changed so that it becomes equal. In this case let's pick the y, but let us write first the system in its format.
$y = {x}^{2}$
$1 + y = 2 x$ ----------> make everything negative so it will be erased the y later

$y = {x}^{2}$
$- 1 - y = - 2 x$

Now we have:
$- 1 = - 2 x + {x}^{2}$ or $0 = {x}^{2} - 2 x + 1$ which is equal to $0 = {\left(x - 1\right)}^{2}$
Now we need to solve for x:
-we cancel the squared expression and use only $x - 1$ which $x = 1$

Now we can solve for y by taking any of the two equations:

• $y = {x}^{2} = {1}^{2} = 1$
-$y = 2 x - 1 = 2 \cdot 1 - 1 = 1$

You have now the solution for both values