Solve {l}{x-4/2-x-3/3=4}{y=x}{text{Solvefor}ztext{where}}{z=y}

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

Solve for x, y, z

$$z=30$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$3\left(x-4\right)-2\left(x-3\right)=24$$

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

$$3x-12-2\left(x-3\right)=24$$

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

$$3x-12-2x+6=24$$

Combine 3x and -2x to get x.

$$x-12+6=24$$

Add -12 and 6 to get -6.

$$x-6=24$$

Add 6 to both sides.

$$x=24+6$$

Add 24 and 6 to get 30.

$$x=30$$

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

$$y=30$$

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

$$z=30$$

The system is now solved.

$$x=30 y=30 z=30$$