Solve {l}{24*3y=2}{6x+17y=12}

$$\left. \begin{array} { l } { 24 \times 3 y = 2 } \\ { 6 x + 17 y = 12 } \end{array} \right.$$

Solve for y, x

$$x = \frac{415}{216} = 1\frac{199}{216} \approx 1.921296296$$

$$y=\frac{1}{36}\approx 0.027777778$$

Solution Steps

Consider the first equation. Multiply 24 and 3 to get 72.

$$72y=2$$

Divide both sides by 72.

$$y=\frac{2}{72}$$

Reduce the fraction \frac{2}{72} to lowest terms by extracting and canceling out 2.

$$y=\frac{1}{36}$$

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

$$6x+17\times \frac{1}{36}=12$$

Multiply 17 and \frac{1}{36} to get \frac{17}{36}.

$$6x+\frac{17}{36}=12$$

Subtract \frac{17}{36} from both sides.

$$6x=12-\frac{17}{36}$$

Subtract \frac{17}{36} from 12 to get \frac{415}{36}.

$$6x=\frac{415}{36}$$

Divide both sides by 6.

$$x=\frac{\frac{415}{36}}{6}$$

Express \frac{\frac{415}{36}}{6} as a single fraction.

$$x=\frac{415}{36\times 6}$$

Multiply 36 and 6 to get 216.

$$x=\frac{415}{216}$$

The system is now solved.

$$y=\frac{1}{36} x=\frac{415}{216}$$