Solve {l}{1+x^2=1/7a}{1+y^2=1/50a}{x+y=1/250a}

$$\left. \begin{array} { l } { 1 + x ^ { 2 } = \frac { 1 } { 7 } a } \\ { 1 + y ^ { 2 } = \frac { 1 } { 50 } a } \\ { x + y = \frac { 1 } { 250 } a } \end{array} \right.$$

Solve for x, a, y (complex solution)

$$x=\frac{250-\sqrt{8701}}{7}\approx 22.388692723\text{, }y=-\frac{\sqrt{8701}}{7}+5\approx -8.325592991\text{, }a=\frac{71250-500\sqrt{8701}}{7}\approx 3515.774932891$$

$$x=\frac{\sqrt{8701}+250}{7}\approx 49.039878706\text{, }y=\frac{\sqrt{8701}}{7}+5\approx 18.325592991\text{, }a=\frac{500\sqrt{8701}+71250}{7}\approx 16841.367924252$$

$$x=i\text{, }y=-i\text{, }a=0$$

$$x=-i\text{, }y=i\text{, }a=0$$

Solve for x, a, y

$$x=\frac{250-\sqrt{8701}}{7}\approx 22.388692723\text{, }y=-\frac{\sqrt{8701}}{7}+5\approx -8.325592991\text{, }a=\frac{71250-500\sqrt{8701}}{7}\approx 3515.774932891$$

$$x=\frac{\sqrt{8701}+250}{7}\approx 49.039878706\text{, }y=\frac{\sqrt{8701}}{7}+5\approx 18.325592991\text{, }a=\frac{500\sqrt{8701}+71250}{7}\approx 16841.367924252$$