Solve {l}{5-2x/x-3=1/3}{y=-6x+12}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{5 - 2 x}{x - 3} = \frac{1}{3} }\\ { y = -6 x + 12 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z = -\frac{24}{7} = -3\frac{3}{7} \approx -3.428571429$$

Solution Steps

Consider the first equation. Variable x cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by 3\left(x-3\right), the least common multiple of x-3,3.

$$3\left(5-2x\right)=x-3$$

Use the distributive property to multiply 3 by 5-2x.

$$15-6x=x-3$$

Subtract x from both sides.

$$15-6x-x=-3$$

Combine -6x and -x to get -7x.

$$15-7x=-3$$

Subtract 15 from both sides.

$$-7x=-3-15$$

Subtract 15 from -3 to get -18.

$$-7x=-18$$

Divide both sides by -7.

$$x=\frac{-18}{-7}$$

Fraction \frac{-18}{-7} can be simplified to \frac{18}{7} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{18}{7}$$

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

$$y=-6\times \frac{18}{7}+12$$

Multiply -6 and \frac{18}{7} to get -\frac{108}{7}.

$$y=-\frac{108}{7}+12$$

Add -\frac{108}{7} and 12 to get -\frac{24}{7}.

$$y=-\frac{24}{7}$$

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

$$z=-\frac{24}{7}$$

The system is now solved.

$$x=\frac{18}{7} y=-\frac{24}{7} z=-\frac{24}{7}$$