Solve {l}{3g+3m=18}{69+4m=32}

$$\left. \begin{array} { l } { 3 g + 3 m = 18 } \\ { 69 + 4 m = 32 } \end{array} \right.$$

Solve for g, m

$$g = \frac{61}{4} = 15\frac{1}{4} = 15.25$$

$$m = -\frac{37}{4} = -9\frac{1}{4} = -9.25$$

Solution Steps

Consider the second equation. Subtract 69 from both sides.

$$4m=32-69$$

Subtract 69 from 32 to get -37.

$$4m=-37$$

Divide both sides by 4.

$$m=-\frac{37}{4}$$

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

$$3g+3\left(-\frac{37}{4}\right)=18$$

Multiply 3 and -\frac{37}{4} to get -\frac{111}{4}.

$$3g-\frac{111}{4}=18$$

Add \frac{111}{4} to both sides.

$$3g=18+\frac{111}{4}$$

Add 18 and \frac{111}{4} to get \frac{183}{4}.

$$3g=\frac{183}{4}$$

Divide both sides by 3.

$$g=\frac{\frac{183}{4}}{3}$$

Express \frac{\frac{183}{4}}{3} as a single fraction.

$$g=\frac{183}{4\times 3}$$

Multiply 4 and 3 to get 12.

$$g=\frac{183}{12}$$

Reduce the fraction \frac{183}{12} to lowest terms by extracting and canceling out 3.

$$g=\frac{61}{4}$$

The system is now solved.

$$g=\frac{61}{4} m=-\frac{37}{4}$$