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

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

Solve for x, y

$$x = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

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

Solution Steps

Consider the second equation. Combine y and 5y to get 6y.

$$6y=2$$

Divide both sides by 6.

$$y=\frac{2}{6}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

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

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

$$2x-\frac{1}{3}=3$$

Add \frac{1}{3} to both sides.

$$2x=3+\frac{1}{3}$$

Add 3 and \frac{1}{3} to get \frac{10}{3}.

$$2x=\frac{10}{3}$$

Divide both sides by 2.

$$x=\frac{\frac{10}{3}}{2}$$

Express \frac{\frac{10}{3}}{2} as a single fraction.

$$x=\frac{10}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$x=\frac{10}{6}$$

Reduce the fraction \frac{10}{6} to lowest terms by extracting and canceling out 2.

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

The system is now solved.

$$x=\frac{5}{3} y=\frac{1}{3}$$