Solve {l}{x-2y=6}{x=log-2}

$$\left. \begin{array}{l}{ x - 2 y = 6 }\\{ x = \log - 2 }\end{array} \right.$$

Solve for x, y (complex solution)

$$x=\log(e)\left(\ln(2)+\pi i\right)\approx 0.301029996+1.364376354i$$

$$y=-\frac{\log(e)\left(-\pi i+\ln(500000)\right)}{2}\approx -2.849485002+0.682188177i$$

Steps Using Substitution

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

$$x=\log_{10}\left(-2\right),x-2y=6$$

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

$$x=\log_{10}\left(-2\right)$$

Divide both sides by 1.

$$x=\log(e)\left(\ln(2)+\pi i\right)$$

Substitute \left(\ln(2)+i\pi \right)\log(e) for x in the other equation, x-2y=6.

$$\log(e)\left(\ln(2)+\pi i\right)-2y=6$$

Subtract \left(\ln(2)+i\pi \right)\log(e) from both sides of the equation.

$$-2y=\log(e)\left(-\pi i+\ln(500000)\right)$$

Divide both sides by -2.

$$y=-\frac{\log(e)\left(-\pi i+\ln(500000)\right)}{2}$$

The system is now solved.

$$x=\log(e)\left(\ln(2)+\pi i\right),y=-\frac{\log(e)\left(-\pi i+\ln(500000)\right)}{2}$$