Solve {l}{x/3+1/4=0.1}{x/3+y/5=0}

$$\left. \begin{array} { l } { \frac { x } { 3 } + \frac { 1 } { 4 } = 0.1 } \\ { \frac { x } { 3 } + \frac { y } { 5 } = 0 } \end{array} \right.$$

Solve for x, y

$$x=-0.45$$

$$y=0.75$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 12, the least common multiple of 3,4.

$$4x+3=1.2$$

Subtract 3 from both sides.

$$4x=1.2-3$$

Subtract 3 from 1.2 to get -1.8.

$$4x=-1.8$$

Divide both sides by 4.

$$x=\frac{-1.8}{4}$$

Expand \frac{-1.8}{4} by multiplying both numerator and the denominator by 10.

$$x=\frac{-18}{40}$$

Reduce the fraction \frac{-18}{40} to lowest terms by extracting and canceling out 2.

$$x=-\frac{9}{20}$$

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

$$\frac{-\frac{9}{20}}{3}+\frac{y}{5}=0$$

Multiply both sides of the equation by 15, the least common multiple of 3,5.

$$5\left(-\frac{9}{20}\right)+3y=0$$

Multiply 5 and -\frac{9}{20} to get -\frac{9}{4}.

$$-\frac{9}{4}+3y=0$$

Add \frac{9}{4} to both sides. Anything plus zero gives itself.

$$3y=\frac{9}{4}$$

Divide both sides by 3.

$$y=\frac{\frac{9}{4}}{3}$$

Express \frac{\frac{9}{4}}{3} as a single fraction.

$$y=\frac{9}{4\times 3}$$

Multiply 4 and 3 to get 12.

$$y=\frac{9}{12}$$

Reduce the fraction \frac{9}{12} to lowest terms by extracting and canceling out 3.

$$y=\frac{3}{4}$$

The system is now solved.

$$x=-\frac{9}{20} y=\frac{3}{4}$$