Solve {l}{5k+11=9}{6m-9=k}

$$\left. \begin{array} { l } { 5 k + 11 = 9 } \\ { 6 m - 9 = k } \end{array} \right.$$

Solve for k, m

$$k=-\frac{2}{5}=-0.4$$

$$m = \frac{43}{30} = 1\frac{13}{30} \approx 1.433333333$$

Solution Steps

Consider the first equation. Subtract 11 from both sides.

$$5k=9-11$$

Subtract 11 from 9 to get -2.

$$5k=-2$$

Divide both sides by 5.

$$k=-\frac{2}{5}$$

Consider the second equation. Insert the known values of variables into the equation.

$$6m-9=-\frac{2}{5}$$

Add 9 to both sides.

$$6m=-\frac{2}{5}+9$$

Add -\frac{2}{5} and 9 to get \frac{43}{5}.

$$6m=\frac{43}{5}$$

Divide both sides by 6.

$$m=\frac{\frac{43}{5}}{6}$$

Express \frac{\frac{43}{5}}{6} as a single fraction.

$$m=\frac{43}{5\times 6}$$

Multiply 5 and 6 to get 30.

$$m=\frac{43}{30}$$

The system is now solved.

$$k=-\frac{2}{5} m=\frac{43}{30}$$