Question

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

Answer 1

`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=2x` ----------> make everything negative so it will be erased the y later

`y=x^2`
`-1-y=-2x`

Now we have:
`-1=-2x+x^2` or `0= x^2-2x+1` which is equal to `0= (x-1)^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=2x-1= 2*1-1=1`

You have now the solution for both values