Solve {l}{x+3x*3/2=20}{y=x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { x + 3 x \cdot \frac{3}{2} = 20 }\\ { y = x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z = \frac{40}{11} = 3\frac{7}{11} \approx 3.636363636$$

Solution Steps

Consider the first equation. Multiply 3 and \frac{3}{2} to get \frac{9}{2}.

$$x+\frac{9}{2}x=20$$

Combine x and \frac{9}{2}x to get \frac{11}{2}x.

$$\frac{11}{2}x=20$$

Multiply both sides by \frac{2}{11}, the reciprocal of \frac{11}{2}.

$$x=20\times \frac{2}{11}$$

Multiply 20 and \frac{2}{11} to get \frac{40}{11}.

$$x=\frac{40}{11}$$

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

$$y=\frac{40}{11}$$

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

$$z=\frac{40}{11}$$

The system is now solved.

$$x=\frac{40}{11} y=\frac{40}{11} z=\frac{40}{11}$$