Solve {l}{7/x=3/x+1}{y=2*1}{text{Solvefor}ztext{where}}{z=y}

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

Solve for x, y, z

$$z=2$$

Solution Steps

Consider the first equation. Variable x cannot be equal to any of the values -1,0 since division by zero is not defined. Multiply both sides of the equation by x\left(x+1\right), the least common multiple of x,x+1.

$$\left(x+1\right)\times 7=x\times 3$$

Use the distributive property to multiply x+1 by 7.

$$7x+7=x\times 3$$

Subtract x\times 3 from both sides.

$$7x+7-x\times 3=0$$

Combine 7x and -x\times 3 to get 4x.

$$4x+7=0$$

Subtract 7 from both sides. Anything subtracted from zero gives its negation.

$$4x=-7$$

Divide both sides by 4.

$$x=-\frac{7}{4}$$

Consider the second equation. Multiply 2 and 1 to get 2.

$$y=2$$

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

$$z=2$$

The system is now solved.

$$x=-\frac{7}{4} y=2 z=2$$