Solve {l}{0x-3y=-5}{4x-y=1}

$$\left. \begin{array} { l } { 0 x - 3 y = - 5 } \\ { 4 x - y = 1 } \end{array} \right.$$

Solve for x, y

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

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

Solution Steps

Consider the first equation. Anything times zero gives zero.

$$0-3y=-5$$

Anything plus zero gives itself.

$$-3y=-5$$

Divide both sides by -3.

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

Fraction \frac{-5}{-3} can be simplified to \frac{5}{3} by removing the negative sign from both the numerator and the denominator.

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

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

$$4x-\frac{5}{3}=1$$

Add \frac{5}{3} to both sides.

$$4x=1+\frac{5}{3}$$

Add 1 and \frac{5}{3} to get \frac{8}{3}.

$$4x=\frac{8}{3}$$

Divide both sides by 4.

$$x=\frac{\frac{8}{3}}{4}$$

Express \frac{\frac{8}{3}}{4} as a single fraction.

$$x=\frac{8}{3\times 4}$$

Multiply 3 and 4 to get 12.

$$x=\frac{8}{12}$$

Reduce the fraction \frac{8}{12} to lowest terms by extracting and canceling out 4.

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

The system is now solved.

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