Solve {l}{x+3/4x-1/2=x-1/12x+1/12}{y=12x-9*4x-5}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{x + 3}{4 x} - \frac{1}{2} = \frac{x - 1}{12 x} + \frac{1}{12} }\\ { y = 12 x - 9 \cdot 4 x - 5 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=-53$$

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 12x, the least common multiple of 4x,2,12x,12.

$$3\left(x+3\right)+12x\left(-\frac{1}{2}\right)=x-1+12x\times \frac{1}{12}$$

Use the distributive property to multiply 3 by x+3.

$$3x+9+12x\left(-\frac{1}{2}\right)=x-1+12x\times \frac{1}{12}$$

Multiply 12 and -\frac{1}{2} to get -6.

$$3x+9-6x=x-1+12x\times \frac{1}{12}$$

Combine 3x and -6x to get -3x.

$$-3x+9=x-1+12x\times \frac{1}{12}$$

Multiply 12 and \frac{1}{12} to get 1.

$$-3x+9=x-1+x$$

Combine x and x to get 2x.

$$-3x+9=2x-1$$

Subtract 2x from both sides.

$$-3x+9-2x=-1$$

Combine -3x and -2x to get -5x.

$$-5x+9=-1$$

Subtract 9 from both sides.

$$-5x=-1-9$$

Subtract 9 from -1 to get -10.

$$-5x=-10$$

Divide both sides by -5.

$$x=\frac{-10}{-5}$$

Divide -10 by -5 to get 2.

$$x=2$$

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

$$y=12\times 2-9\times 4\times 2-5$$

Multiply 12 and 2 to get 24.

$$y=24-9\times 4\times 2-5$$

Multiply 9 and 4 to get 36.

$$y=24-36\times 2-5$$

Multiply 36 and 2 to get 72.

$$y=24-72-5$$

Subtract 72 from 24 to get -48.

$$y=-48-5$$

Subtract 5 from -48 to get -53.

$$y=-53$$

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

$$z=-53$$

The system is now solved.

$$x=2 y=-53 z=-53$$