Solve {l}{frac{{(2w+3)}}{5}=frac{{(w-2)}}{3}}{x=w}{text{Solvefor}ytext{where}}{y=x}

$$\left. \begin{array} { l } { \frac{{(2 w + 3)}}{5} = \frac{{(w - 2)}}{3} }\\ { x = w }\\ { \text{Solve for } y \text{ where} } \\ { y = x } \end{array} \right.$$

Solve for w, x, y

$$y=-19$$

Solution Steps

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

$$3\left(2w+3\right)=5\left(w-2\right)$$

Use the distributive property to multiply 3 by 2w+3.

$$6w+9=5\left(w-2\right)$$

Use the distributive property to multiply 5 by w-2.

$$6w+9=5w-10$$

Subtract 5w from both sides.

$$6w+9-5w=-10$$

Combine 6w and -5w to get w.

$$w+9=-10$$

Subtract 9 from both sides.

$$w=-10-9$$

Subtract 9 from -10 to get -19.

$$w=-19$$

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

$$x=-19$$

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

$$y=-19$$

The system is now solved.

$$w=-19 x=-19 y=-19$$