Solve {l}{m=-frac{2sqrt{5}}{5}-4}{y=-1/2m-2}

$$\left. \begin{array} { l } { m = - \frac { 2 \sqrt { 5 } } { 5 } - 4 } \\ { y = - \frac { 1 } { 2 } m - 2 } \end{array} \right.$$

Solve for m, y

$$y=\frac{\sqrt{5}}{5}\approx 0.447213595$$

$$m=-\frac{2\sqrt{5}}{5}-4\approx -4.894427191$$

Steps Using Substitution

Consider the second equation. Add \frac{1}{2}m to both sides.

$$y+\frac{1}{2}m=-2$$

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.

$$m=-\frac{2\sqrt{5}}{5}-4,\frac{1}{2}m+y=-2$$

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

$$m=-\frac{2\sqrt{5}}{5}-4$$

Substitute -\frac{2\sqrt{5}}{5}-4 for m in the other equation, \frac{1}{2}m+y=-2.

$$\frac{1}{2}\left(-\frac{2\sqrt{5}}{5}-4\right)+y=-2$$

Multiply \frac{1}{2} times -\frac{2\sqrt{5}}{5}-4.

$$-\frac{\sqrt{5}}{5}-2+y=-2$$

Subtract -\frac{\sqrt{5}}{5}-2 from both sides of the equation.

$$y=\frac{\sqrt{5}}{5}$$

The system is now solved.

$$m=-\frac{2\sqrt{5}}{5}-4,y=\frac{\sqrt{5}}{5}$$