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

1 Answer
Rene
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=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

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