Stimultaneous equations (squared)

x-2y=-2       x^2-y^2=7

$$x-2y=-2 \qquad x=2y-2 \\\\
x^2-y^2=7 \qquad (2y-2)^2-y^2=7\\
4y^2-8y+4-y^2=7\\
3y^2-8y+4=7\\
3y^2-8y-3=0\\\\
\small{\text{
$
y_{1,2}=\dfrac{8\pm\sqrt{64-4*3*(-3)} } {2*3}
=\dfrac{8\pm\sqrt{64-36} } {6}
=\dfrac{8\pm\sqrt{100} } {6}
=\dfrac{8\pm10 } {6}
$
}}\\\\
\small{\text{
$
y_1=\dfrac{8+10 } {6}=\dfrac{18 } {6}=3
$
}}\\\\
\small{\text{
$
y_2=\dfrac{8-10}{6}=-\dfrac{2}{6}=-\dfrac{1}{3}
$
}}\\\\
\small{\text{
$
x_1=2*3-2 = 4
$
}}\\
\small{\text{
$
x_2=2*(-\frac{1}{3})-2 = -2\frac{2}{3}
$
}}$$