Answer
$$x = 7, y = 9$$
Work Step by Step
Writing the equation:
$x^{2} + y^{2} = 130$ (equation 1)
$x^{2} - y^{2} = 32$ (equation 2)
Simultaneously solving the equation will eliminate the term $y^{2}$, which will yield an equation: $$2x^{2} = 98$$
Divide both sides by two:
$$\frac{2x^{2}}{2} = \frac{98}{2}$$ $$x^{2} = 49$$ $$x = 7$$
Substituting to equation 1: $$x^{2} + y^{2} = 130$$ $$7^{2} + y^{2} = 130$$ $$49 + y^{2} = 130$$
Subtract $49$ to both sides:
$$49 -49+ y^{2} = 130-49$$ $$y^{2} = 81$$ $$y = 9$$
