Solve {l}{9x+7/2-{(x-x-2/7)}=36}{y=6x+1*7x-3}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{9 x + 7}{2} - {(x - \frac{x - 2}{7})} = 36 }\\ { y = 6 x + 1 \cdot 7 x - 3 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=114$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 14, the least common multiple of 2,7.

$$7\left(9x+7\right)-14\left(x-\frac{x-2}{7}\right)=504$$

Use the distributive property to multiply 7 by 9x+7.

$$63x+49-14\left(x-\frac{x-2}{7}\right)=504$$

Divide each term of x-2 by 7 to get \frac{1}{7}x-\frac{2}{7}.

$$63x+49-14\left(x-\left(\frac{1}{7}x-\frac{2}{7}\right)\right)=504$$

To find the opposite of \frac{1}{7}x-\frac{2}{7}, find the opposite of each term.

$$63x+49-14\left(x-\frac{1}{7}x+\frac{2}{7}\right)=504$$

Combine x and -\frac{1}{7}x to get \frac{6}{7}x.

$$63x+49-14\left(\frac{6}{7}x+\frac{2}{7}\right)=504$$

Use the distributive property to multiply -14 by \frac{6}{7}x+\frac{2}{7}.

$$63x+49-12x-4=504$$

Combine 63x and -12x to get 51x.

$$51x+49-4=504$$

Subtract 4 from 49 to get 45.

$$51x+45=504$$

Subtract 45 from both sides.

$$51x=504-45$$

Subtract 45 from 504 to get 459.

$$51x=459$$

Divide both sides by 51.

$$x=\frac{459}{51}$$

Divide 459 by 51 to get 9.

$$x=9$$

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

$$y=6\times 9+1\times 7\times 9-3$$

Do the multiplications.

$$y=54+7\times 9-3$$

Multiply 7 and 9 to get 63.

$$y=54+63-3$$

Add 54 and 63 to get 117.

$$y=117-3$$

Subtract 3 from 117 to get 114.

$$y=114$$

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

$$z=114$$

The system is now solved.

$$x=9 y=114 z=114$$