Solve {l}{3/5+y/3=7}{y/5-x/2=-2}

$$\left\{ \begin{array} { l } { \frac { 3 } { 5 } + \frac { y } { 3 } = 7 } \\ { \frac { y } { 5 } - \frac { x } { 2 } = - 2 } \end{array} \right.$$

Solve for y, x

$$x = \frac{292}{25} = 11\frac{17}{25} = 11.68$$

$$y = \frac{96}{5} = 19\frac{1}{5} = 19.2$$

Solution Steps

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

$$9+5y=105$$

Subtract 9 from both sides.

$$5y=105-9$$

Subtract 9 from 105 to get 96.

$$5y=96$$

Divide both sides by 5.

$$y=\frac{96}{5}$$

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

$$\frac{\frac{96}{5}}{5}-\frac{x}{2}=-2$$

Multiply both sides of the equation by 10, the least common multiple of 5,2.

$$2\times \frac{96}{5}-5x=-20$$

Multiply 2 and \frac{96}{5} to get \frac{192}{5}.

$$\frac{192}{5}-5x=-20$$

Subtract \frac{192}{5} from both sides.

$$-5x=-20-\frac{192}{5}$$

Subtract \frac{192}{5} from -20 to get -\frac{292}{5}.

$$-5x=-\frac{292}{5}$$

Divide both sides by -5.

$$x=\frac{-\frac{292}{5}}{-5}$$

Express \frac{-\frac{292}{5}}{-5} as a single fraction.

$$x=\frac{-292}{5\left(-5\right)}$$

Multiply 5 and -5 to get -25.

$$x=\frac{-292}{-25}$$

Fraction \frac{-292}{-25} can be simplified to \frac{292}{25} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{292}{25}$$

The system is now solved.

$$y=\frac{96}{5} x=\frac{292}{25}$$