Solve {l}{a^7+x=y}{x+y^2=3}{8+x=4}

$$\left\{ \begin{array} { l } { a ^ { 7 } + x = y } \\ { x + y ^ { 2 } = 3 } \\ { 8 + x = 4 } \end{array} \right.$$

Solve for a, x, y (complex solution)

$$x=-4\text{, }y=-\sqrt{7}\approx -2.645751311\text{, }a=\sqrt[7]{4-\sqrt{7}}\approx 1.044273027$$

$$x=-4\text{, }y=-\sqrt{7}\approx -2.645751311\text{, }a=e^{\frac{2\pi i}{7}}\sqrt[7]{4-\sqrt{7}}\approx 0.651093583+0.816445529i$$

$$x=-4\text{, }y=-\sqrt{7}\approx -2.645751311\text{, }a=e^{\frac{4\pi i}{7}}\sqrt[7]{4-\sqrt{7}}\approx -0.232372609+1.018090922i$$

$$x=-4\text{, }y=-\sqrt{7}\approx -2.645751311\text{, }a=e^{\frac{6\pi i}{7}}\sqrt[7]{4-\sqrt{7}}\approx -0.940857487+0.453093086i$$

$$x=-4\text{, }y=-\sqrt{7}\approx -2.645751311\text{, }a=e^{\frac{8\pi i}{7}}\sqrt[7]{4-\sqrt{7}}\approx -0.940857487-0.453093086i$$

$$x=-4\text{, }y=-\sqrt{7}\approx -2.645751311\text{, }a=e^{\frac{10\pi i}{7}}\sqrt[7]{4-\sqrt{7}}\approx -0.232372609-1.018090922i$$

$$x=-4\text{, }y=-\sqrt{7}\approx -2.645751311\text{, }a=e^{\frac{12\pi i}{7}}\sqrt[7]{4-\sqrt{7}}\approx 0.651093583-0.816445529i$$

$$x=-4\text{, }y=\sqrt{7}\approx 2.645751311\text{, }a=\sqrt[7]{\sqrt{7}+4}\approx 1.31070905$$

$$x=-4\text{, }y=\sqrt{7}\approx 2.645751311\text{, }a=e^{\frac{2\pi i}{7}}\sqrt[7]{\sqrt{7}+4}\approx 0.817213726+1.024753599i$$

$$x=-4\text{, }y=\sqrt{7}\approx 2.645751311\text{, }a=e^{\frac{4\pi i}{7}}\sqrt[7]{\sqrt{7}+4}\approx -0.291660202+1.277846837i$$

$$x=-4\text{, }y=\sqrt{7}\approx 2.645751311\text{, }a=e^{\frac{6\pi i}{7}}\sqrt[7]{\sqrt{7}+4}\approx -1.180908049+0.568695343i$$

$$x=-4\text{, }y=\sqrt{7}\approx 2.645751311\text{, }a=e^{\frac{8\pi i}{7}}\sqrt[7]{\sqrt{7}+4}\approx -1.180908049-0.568695343i$$

$$x=-4\text{, }y=\sqrt{7}\approx 2.645751311\text{, }a=e^{\frac{10\pi i}{7}}\sqrt[7]{\sqrt{7}+4}\approx -0.291660202-1.277846837i$$

$$x=-4\text{, }y=\sqrt{7}\approx 2.645751311\text{, }a=e^{\frac{12\pi i}{7}}\sqrt[7]{\sqrt{7}+4}\approx 0.817213726-1.024753599i$$

Solve for a, x, y

$$x=-4\text{, }y=-\sqrt{7}\approx -2.645751311\text{, }a=\sqrt[7]{4-\sqrt{7}}\approx 1.044273027$$

$$x=-4\text{, }y=\sqrt{7}\approx 2.645751311\text{, }a=\sqrt[7]{\sqrt{7}+4}\approx 1.31070905$$