Answer
The solution is $(1,1)$.
Work Step by Step
The given system is
$y=2x-1$ ...... (1)
$y=x^2$ ...... (2)
Subtract equation (1) from equation (2).
$\Rightarrow y-y=x^2-(2x-1)$
$\Rightarrow y-y=x^2-2x+1$
Simplify.
$\Rightarrow 0=x^2-2x+1$
Write the right terms as square of the polynomial.
$\Rightarrow 0=(x-1)^2$
Take square root on each side.
$\Rightarrow 0=x-1$
Solve for $x$.
$\Rightarrow x=1$
Substitute $1$ for $x$ in equation (1).
$\Rightarrow y=2(1)-1$
Simplify.
$\Rightarrow y=2-1$
$\Rightarrow y=1$
Hence, the solution is $(1,1)$.
