Solve {l}{10-4{(2x-1)}=-2{(3-x)}}{y=x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 10 - 4 {(2 x - 1)} = -2 {(3 - x)} }\\ { y = x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=2$$

Solution Steps

Consider the first equation. Use the distributive property to multiply -4 by 2x-1.

$$10-8x+4=-2\left(3-x\right)$$

Add 10 and 4 to get 14.

$$14-8x=-2\left(3-x\right)$$

Use the distributive property to multiply -2 by 3-x.

$$14-8x=-6+2x$$

Subtract 2x from both sides.

$$14-8x-2x=-6$$

Combine -8x and -2x to get -10x.

$$14-10x=-6$$

Subtract 14 from both sides.

$$-10x=-6-14$$

Subtract 14 from -6 to get -20.

$$-10x=-20$$

Divide both sides by -10.

$$x=\frac{-20}{-10}$$

Divide -20 by -10 to get 2.

$$x=2$$

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

$$y=2$$

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

$$z=2$$

The system is now solved.

$$x=2 y=2 z=2$$