Answer
$(-1,0)$
Work Step by Step
$y=x+1$ Equation $(1)$
$x^{2}-y^{2}=1$ Equation $(2)$
Substitute $y=x+1$ in Equation $(2)$
$x^{2}-y^{2}=1$
$x^{2}-(x+1)^{2}=1$
Using $(a+b)^{2} = a^{2}+2ab+b^{2}$
$(x+1)^{2} =x^{2}+2x(1)+1^{2} = x^{2}+2x+1$
$x^{2}-(x^{2}+2x+1)=1$
$x^{2}-x^{2}-2x-1-1=0$
$-2x-2=0$
$-2(x+1)=0$
$x= -1$
Substitute $ x$ value in Equation $(1)$ to get $y$
$y=x+1$
$y=-1+1$
$y = 0$
$(-1,0)$ satisfy the given equations. $(-1,0)$ is the solution.
