Solve {l}{3/5+2/7+9/x=13/35}{y=x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{3}{5} + \frac{2}{7} + \frac{9}{x} = \frac{13}{35} }\\ { y = x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z = -\frac{35}{2} = -17\frac{1}{2} = -17.5$$

Solution Steps

Consider the first equation. Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 35x, the least common multiple of 5,7,x,35.

$$35x\times \frac{3}{5}+35x\times \frac{2}{7}+35\times 9=13x$$

Multiply 35 and \frac{3}{5} to get 21.

$$21x+35x\times \frac{2}{7}+35\times 9=13x$$

Multiply 35 and \frac{2}{7} to get 10.

$$21x+10x+35\times 9=13x$$

Combine 21x and 10x to get 31x.

$$31x+35\times 9=13x$$

Multiply 35 and 9 to get 315.

$$31x+315=13x$$

Subtract 13x from both sides.

$$31x+315-13x=0$$

Combine 31x and -13x to get 18x.

$$18x+315=0$$

Subtract 315 from both sides. Anything subtracted from zero gives its negation.

$$18x=-315$$

Divide both sides by 18.

$$x=\frac{-315}{18}$$

Reduce the fraction \frac{-315}{18} to lowest terms by extracting and canceling out 9.

$$x=-\frac{35}{2}$$

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

$$y=-\frac{35}{2}$$

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

$$z=-\frac{35}{2}$$

The system is now solved.

$$x=-\frac{35}{2} y=-\frac{35}{2} z=-\frac{35}{2}$$