Solve {l}{6{(x+2)}-{(0*4x-0*6)}=0*2{(1-x)}}{y=0}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 6 {(x + 2)} - {(0 \cdot 4 x - 0 \cdot 6)} = 0 \cdot 2 {(1 - x)} }\\ { y = 0 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=0$$

Solution Steps

Consider the first equation. Use the distributive property to multiply 6 by x+2.

$$6x+12-\left(0\times 4x-0\times 6\right)=0\times 2\left(1-x\right)$$

Multiply 0 and 4 to get 0.

$$6x+12-\left(0x-0\times 6\right)=0\times 2\left(1-x\right)$$

Anything times zero gives zero.

$$6x+12-\left(0-0\times 6\right)=0\times 2\left(1-x\right)$$

Multiply 0 and 6 to get 0.

$$6x+12-\left(0-0\right)=0\times 2\left(1-x\right)$$

Subtracting 0 from itself leaves 0.

$$6x+12-0=0\times 2\left(1-x\right)$$

Multiply 0 and 2 to get 0.

$$6x+12-0=0\left(1-x\right)$$

Anything times zero gives zero.

$$6x+12-0=0$$

Add 0 to both sides.

$$6x+12=0+0$$

Add 0 and 0 to get 0.

$$6x+12=0$$

Subtract 12 from both sides. Anything subtracted from zero gives its negation.

$$6x=-12$$

Divide both sides by 6.

$$x=\frac{-12}{6}$$

Divide -12 by 6 to get -2.

$$x=-2$$

The system is now solved.

$$x=-2 y=0 z=0$$