Solve {l}{3x+1=2}{x+y=3}

$$\left\{ \begin{array} { l } { 3 x + 1 = 2 } \\ { x + y = 3 } \end{array} \right.$$

Solve for x, y

$$x=\frac{1}{3}\approx 0.333333333$$

$$y = \frac{8}{3} = 2\frac{2}{3} \approx 2.666666667$$

Solution Steps

Consider the first equation. Subtract 1 from both sides.

$$3x=2-1$$

Subtract 1 from 2 to get 1.

$$3x=1$$

Divide both sides by 3.

$$x=\frac{1}{3}$$

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

$$\frac{1}{3}+y=3$$

Subtract \frac{1}{3} from both sides.

$$y=3-\frac{1}{3}$$

Subtract \frac{1}{3} from 3 to get \frac{8}{3}.

$$y=\frac{8}{3}$$

The system is now solved.

$$x=\frac{1}{3} y=\frac{8}{3}$$