Solve {l}{y/5=13/10}{1.2/m=3/5}{frac{6.3}{x}=frac{18}{5}}

$$\left. \begin{array} { l } { \frac { y } { 5 } = \frac { 13 } { 10 } } \\ { \frac { 1.2 } { m } = \frac { 3 } { 5 } } \\ { \frac { 6.3 } { x } = \frac { 18 } { 5 } } \end{array} \right.$$

Solve for y, m, x

$$x=1.75$$

$$y=6.5$$

$$m=2$$

Solution Steps

Consider the first equation. Multiply both sides by 5.

$$y=\frac{13}{10}\times 5$$

Multiply \frac{13}{10} and 5 to get \frac{13}{2}.

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

Consider the second equation. Variable m cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 5m, the least common multiple of m,5.

$$5\times 1.2=3m$$

Multiply 5 and 1.2 to get 6.

$$6=3m$$

Swap sides so that all variable terms are on the left hand side.

$$3m=6$$

Divide both sides by 3.

$$m=\frac{6}{3}$$

Divide 6 by 3 to get 2.

$$m=2$$

Consider the third equation. Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 5x, the least common multiple of x,5.

$$5\times 6.3=18x$$

Multiply 5 and 6.3 to get 31.5.

$$31.5=18x$$

Swap sides so that all variable terms are on the left hand side.

$$18x=31.5$$

Divide both sides by 18.

$$x=\frac{31.5}{18}$$

Expand \frac{31.5}{18} by multiplying both numerator and the denominator by 10.

$$x=\frac{315}{180}$$

Reduce the fraction \frac{315}{180} to lowest terms by extracting and canceling out 45.

$$x=\frac{7}{4}$$

The system is now solved.

$$y=\frac{13}{2} m=2 x=\frac{7}{4}$$