Solve {l}{2xy=7}{1y=sum_k=0^12e^k}

$$\left. \begin{array} { l } { 2 x y = 7 } \\ { 1 y = \sum _ { k = 0 } ^ { 12 } e ^ { k } } \end{array} \right.$$

Solve for x, y

$$x=-\frac{7\left(1-e\right)}{2\left(e^{13}-1\right)}\approx 0.000013594$$

$$y=\frac{e^{13}-1}{e-1}\approx 257473.706979533$$

Steps Using Substitution

Pick one of the two equations which is more simple to solve for y by isolating y on the left hand side of the equal sign.

$$y=\frac{e^{13}-1}{e-1}$$

Substitute \frac{e^{13}-1}{e-1} for y in 2yx=7. Because the resulting equation contains only one variable, you can solve for x directly.

$$2\times \frac{e^{13}-1}{e-1}x=7$$

Multiply 2 times \frac{e^{13}-1}{e-1}.

$$\frac{2\left(e^{13}-1\right)}{e-1}x=7$$

Divide 7 by \frac{2\left(e^{13}-1\right)}{e-1}.

$$x=\frac{7\left(e-1\right)}{2\left(e^{13}-1\right)}$$

The system is now solved.

$$y=\frac{e^{13}-1}{e-1},x=\frac{7\left(e-1\right)}{2\left(e^{13}-1\right)}$$