Solve {l}{x/3+x/2=15}{y=6*x}{z=6*x}{text{Solvefor}a,btext{where}}{a=y}{b=z}

$$\left. \begin{array} { l } { \frac{x}{3} + \frac{x}{2} = 15 }\\ { y = 6 \cdot x }\\ { z = 6 \cdot x }\\ { \text{Solve for } a,b \text{ where} } \\ { a = y }\\ { b = z } \end{array} \right.$$

Solve for x, y, z, a, b

$$a=108$$

$$b=108$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$2x+3x=90$$

Combine 2x and 3x to get 5x.

$$5x=90$$

Divide both sides by 5.

$$x=\frac{90}{5}$$

Divide 90 by 5 to get 18.

$$x=18$$

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

$$y=6\times 18$$

Multiply 6 and 18 to get 108.

$$y=108$$

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

$$z=6\times 18$$

Multiply 6 and 18 to get 108.

$$z=108$$

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

$$a=108$$

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

$$b=108$$

The system is now solved.

$$x=18 y=108 z=108 a=108 b=108$$