Solve {l}{4c+2d=11}{7/2d=4-22}

$$\left. \begin{array} { l } { 4 c + 2 d = 11 } \\ { \frac { 7 } { 2 } d = 4 - 22 } \end{array} \right.$$

Solve for c, d

$$c = \frac{149}{28} = 5\frac{9}{28} \approx 5.321428571$$

$$d = -\frac{36}{7} = -5\frac{1}{7} \approx -5.142857143$$

Solution Steps

Consider the second equation. Subtract 22 from 4 to get -18.

$$\frac{7}{2}d=-18$$

Multiply both sides by \frac{2}{7}, the reciprocal of \frac{7}{2}.

$$d=-18\times \frac{2}{7}$$

Multiply -18 and \frac{2}{7} to get -\frac{36}{7}.

$$d=-\frac{36}{7}$$

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

$$4c+2\left(-\frac{36}{7}\right)=11$$

Multiply 2 and -\frac{36}{7} to get -\frac{72}{7}.

$$4c-\frac{72}{7}=11$$

Add \frac{72}{7} to both sides.

$$4c=11+\frac{72}{7}$$

Add 11 and \frac{72}{7} to get \frac{149}{7}.

$$4c=\frac{149}{7}$$

Divide both sides by 4.

$$c=\frac{\frac{149}{7}}{4}$$

Express \frac{\frac{149}{7}}{4} as a single fraction.

$$c=\frac{149}{7\times 4}$$

Multiply 7 and 4 to get 28.

$$c=\frac{149}{28}$$

The system is now solved.

$$c=\frac{149}{28} d=-\frac{36}{7}$$