Solve {l}{2{(1-x)}=-6x+5{(x-2)}}{y=60{(1/10x+2/3x)}}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 2 {(1 - x)} = -6 x + 5 {(x - 2)} }\\ { y = 60 {(\frac{1}{10} x + \frac{2}{3} x)} }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=552$$

Solution Steps

Consider the first equation. Use the distributive property to multiply 2 by 1-x.

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

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

$$2-2x=-6x+5x-10$$

Combine -6x and 5x to get -x.

$$2-2x=-x-10$$

Add x to both sides.

$$2-2x+x=-10$$

Combine -2x and x to get -x.

$$2-x=-10$$

Subtract 2 from both sides.

$$-x=-10-2$$

Subtract 2 from -10 to get -12.

$$-x=-12$$

Divide both sides by -1.

$$x=\frac{-12}{-1}$$

Fraction \frac{-12}{-1} can be simplified to 12 by removing the negative sign from both the numerator and the denominator.

$$x=12$$

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

$$y=60\left(\frac{1}{10}\times 12+\frac{2}{3}\times 12\right)$$

Multiply \frac{1}{10} and 12 to get \frac{6}{5}.

$$y=60\left(\frac{6}{5}+\frac{2}{3}\times 12\right)$$

Multiply \frac{2}{3} and 12 to get 8.

$$y=60\left(\frac{6}{5}+8\right)$$

Add \frac{6}{5} and 8 to get \frac{46}{5}.

$$y=60\times \frac{46}{5}$$

Multiply 60 and \frac{46}{5} to get 552.

$$y=552$$

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

$$z=552$$

The system is now solved.

$$x=12 y=552 z=552$$