Solve {c}{3y+2=9}{2x+y=4}

$$\left. \begin{array} { c } { 3 y + 2 = 9 } \\ { 2 x + y = 4 } \end{array} \right.$$

Solve for y, x

$$x=\frac{5}{6}\approx 0.833333333$$

$$y = \frac{7}{3} = 2\frac{1}{3} \approx 2.333333333$$

Solution Steps

Consider the first equation. Subtract 2 from both sides.

$$3y=9-2$$

Subtract 2 from 9 to get 7.

$$3y=7$$

Divide both sides by 3.

$$y=\frac{7}{3}$$

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

$$2x+\frac{7}{3}=4$$

Subtract \frac{7}{3} from both sides.

$$2x=4-\frac{7}{3}$$

Subtract \frac{7}{3} from 4 to get \frac{5}{3}.

$$2x=\frac{5}{3}$$

Divide both sides by 2.

$$x=\frac{\frac{5}{3}}{2}$$

Express \frac{\frac{5}{3}}{2} as a single fraction.

$$x=\frac{5}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$x=\frac{5}{6}$$

The system is now solved.

$$y=\frac{7}{3} x=\frac{5}{6}$$