Solve {l}{15y=6{(5y-2/5)}}{text{Solvefor}ztext{where}}{z=1}

$$\left. \begin{array} { l } { 15 y = 6 {(5 y - \frac{2}{5})} }\\ { \text{Solve for } z \text{ where} } \\ { z = 1 } \end{array} \right.$$

Solve for y, z

$$z=1$$

Solution Steps

Consider the first equation. Use the distributive property to multiply 6 by 5y-\frac{2}{5}.

$$15y=30y-\frac{12}{5}$$

Subtract 30y from both sides.

$$15y-30y=-\frac{12}{5}$$

Combine 15y and -30y to get -15y.

$$-15y=-\frac{12}{5}$$

Divide both sides by -15.

$$y=\frac{-\frac{12}{5}}{-15}$$

Express \frac{-\frac{12}{5}}{-15} as a single fraction.

$$y=\frac{-12}{5\left(-15\right)}$$

Multiply 5 and -15 to get -75.

$$y=\frac{-12}{-75}$$

Reduce the fraction \frac{-12}{-75} to lowest terms by extracting and canceling out -3.

$$y=\frac{4}{25}$$

The system is now solved.

$$y=\frac{4}{25} z=1$$