Solve {l}{x-5/12-3x+1/6=4x-3/3-5x+1/4}{y=x+4-x-1x+3*15}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{x - 5}{12} - \frac{3 x + 1}{6} = \frac{4 x - 3}{3} - \frac{5 x + 1}{4} }\\ { y = x + 4 - x - 1 x + 3 \cdot 15 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z = \frac{143}{3} = 47\frac{2}{3} \approx 47.666666667$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 12, the least common multiple of 12,6,3,4.

$$x-5-2\left(3x+1\right)=4\left(4x-3\right)-3\left(5x+1\right)$$

Use the distributive property to multiply -2 by 3x+1.

$$x-5-6x-2=4\left(4x-3\right)-3\left(5x+1\right)$$

Combine x and -6x to get -5x.

$$-5x-5-2=4\left(4x-3\right)-3\left(5x+1\right)$$

Subtract 2 from -5 to get -7.

$$-5x-7=4\left(4x-3\right)-3\left(5x+1\right)$$

Use the distributive property to multiply 4 by 4x-3.

$$-5x-7=16x-12-3\left(5x+1\right)$$

Use the distributive property to multiply -3 by 5x+1.

$$-5x-7=16x-12-15x-3$$

Combine 16x and -15x to get x.

$$-5x-7=x-12-3$$

Subtract 3 from -12 to get -15.

$$-5x-7=x-15$$

Subtract x from both sides.

$$-5x-7-x=-15$$

Combine -5x and -x to get -6x.

$$-6x-7=-15$$

Add 7 to both sides.

$$-6x=-15+7$$

Add -15 and 7 to get -8.

$$-6x=-8$$

Divide both sides by -6.

$$x=\frac{-8}{-6}$$

Reduce the fraction \frac{-8}{-6} to lowest terms by extracting and canceling out -2.

$$x=\frac{4}{3}$$

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

$$y=\frac{4}{3}+4-\frac{4}{3}-\frac{4}{3}+3\times 15$$

Add \frac{4}{3} and 4 to get \frac{16}{3}.

$$y=\frac{16}{3}-\frac{4}{3}-\frac{4}{3}+3\times 15$$

Subtract \frac{4}{3} from \frac{16}{3} to get 4.

$$y=4-\frac{4}{3}+3\times 15$$

Subtract \frac{4}{3} from 4 to get \frac{8}{3}.

$$y=\frac{8}{3}+3\times 15$$

Multiply 3 and 15 to get 45.

$$y=\frac{8}{3}+45$$

Add \frac{8}{3} and 45 to get \frac{143}{3}.

$$y=\frac{143}{3}$$

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

$$z=\frac{143}{3}$$

The system is now solved.

$$x=\frac{4}{3} y=\frac{143}{3} z=\frac{143}{3}$$