Solve {l}{x/8-1/5=-1/10}{x/5-frac{y}{4}=-frac{69}{40}}

$$\left\{ \begin{array} { l } { \frac { x } { 8 } - \frac { 1 } { 5 } = - \frac { 1 } { 10 } } \\ { \frac { x } { 5 } - \frac { y } { 4 } = - \frac { 69 } { 40 } } \end{array} \right.$$

Solve for x, y

$$x=\frac{4}{5}=0.8$$

$$y = \frac{377}{50} = 7\frac{27}{50} = 7.54$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 40, the least common multiple of 8,5,10.

$$5x-8=-4$$

Add 8 to both sides.

$$5x=-4+8$$

Add -4 and 8 to get 4.

$$5x=4$$

Divide both sides by 5.

$$x=\frac{4}{5}$$

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

$$\frac{\frac{4}{5}}{5}-\frac{y}{4}=-\frac{69}{40}$$

Multiply both sides of the equation by 40, the least common multiple of 5,4,40.

$$8\times \frac{4}{5}-10y=-69$$

Multiply 8 and \frac{4}{5} to get \frac{32}{5}.

$$\frac{32}{5}-10y=-69$$

Subtract \frac{32}{5} from both sides.

$$-10y=-69-\frac{32}{5}$$

Subtract \frac{32}{5} from -69 to get -\frac{377}{5}.

$$-10y=-\frac{377}{5}$$

Divide both sides by -10.

$$y=\frac{-\frac{377}{5}}{-10}$$

Express \frac{-\frac{377}{5}}{-10} as a single fraction.

$$y=\frac{-377}{5\left(-10\right)}$$

Multiply 5 and -10 to get -50.

$$y=\frac{-377}{-50}$$

Fraction \frac{-377}{-50} can be simplified to \frac{377}{50} by removing the negative sign from both the numerator and the denominator.

$$y=\frac{377}{50}$$

The system is now solved.

$$x=\frac{4}{5} y=\frac{377}{50}$$