Solve {l}{3*{(5-x)}-1/7*{(2*1x-0*77)}=0*0*9-2x}{y=4}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 3 \cdot {(5 - x)} - \frac{1}{7} \cdot {(2 \cdot 1 x - 0 \cdot 77)} = 0 \cdot 0 \cdot 9 - 2 x }\\ { y = 4 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=4$$

Solution Steps

Consider the first equation. Use the distributive property to multiply 3 by 5-x.

$$15-3x-\frac{1}{7}\left(2\times 1x-0\times 77\right)=0\times 0\times 9-2x$$

Multiply 2 and 1 to get 2.

$$15-3x-\frac{1}{7}\left(2x-0\times 77\right)=0\times 0\times 9-2x$$

Multiply 0 and 77 to get 0.

$$15-3x-\frac{1}{7}\left(2x-0\right)=0\times 0\times 9-2x$$

Multiply 0 and 0 to get 0.

$$15-3x-\frac{1}{7}\left(2x-0\right)=0\times 9-2x$$

Multiply 0 and 9 to get 0.

$$15-3x-\frac{1}{7}\left(2x-0\right)=0-2x$$

Anything plus zero gives itself.

$$15-3x-\frac{1}{7}\left(2x-0\right)=-2x$$

Add 2x to both sides.

$$15-3x-\frac{1}{7}\left(2x-0\right)+2x=0$$

Reorder the terms.

$$-3x+15-\frac{1}{7}\times 2x+2x=0$$

Multiply -\frac{1}{7} and 2 to get -\frac{2}{7}.

$$-3x+15-\frac{2}{7}x+2x=0$$

Combine -3x and -\frac{2}{7}x to get -\frac{23}{7}x.

$$-\frac{23}{7}x+15+2x=0$$

Combine -\frac{23}{7}x and 2x to get -\frac{9}{7}x.

$$-\frac{9}{7}x+15=0$$

Subtract 15 from both sides. Anything subtracted from zero gives its negation.

$$-\frac{9}{7}x=-15$$

Multiply both sides by -\frac{7}{9}, the reciprocal of -\frac{9}{7}.

$$x=-15\left(-\frac{7}{9}\right)$$

Multiply -15 and -\frac{7}{9} to get \frac{35}{3}.

$$x=\frac{35}{3}$$

The system is now solved.

$$x=\frac{35}{3} y=4 z=4$$