Solve {l}{3x-1=1}{x+2y=5}

$$\left. \begin{array} { l } { 3 x - 1 = 1 } \\ { x + 2 y = 5 } \end{array} \right.$$

Solve for x, y

$$x=\frac{2}{3}\approx 0.666666667$$

$$y = \frac{13}{6} = 2\frac{1}{6} \approx 2.166666667$$

Solution Steps

Consider the first equation. Add 1 to both sides.

$$3x=1+1$$

Add 1 and 1 to get 2.

$$3x=2$$

Divide both sides by 3.

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

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

$$\frac{2}{3}+2y=5$$

Subtract \frac{2}{3} from both sides.

$$2y=5-\frac{2}{3}$$

Subtract \frac{2}{3} from 5 to get \frac{13}{3}.

$$2y=\frac{13}{3}$$

Divide both sides by 2.

$$y=\frac{\frac{13}{3}}{2}$$

Express \frac{\frac{13}{3}}{2} as a single fraction.

$$y=\frac{13}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$y=\frac{13}{6}$$

The system is now solved.

$$x=\frac{2}{3} y=\frac{13}{6}$$