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

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

Solve for x, y, z

$$z=33$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 20, the least common multiple of 4,2,5.

$$5\left(3x-1\right)-10\left(x-1\right)=4\left(x-2\right)-20$$

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

$$15x-5-10\left(x-1\right)=4\left(x-2\right)-20$$

Use the distributive property to multiply -10 by x-1.

$$15x-5-10x+10=4\left(x-2\right)-20$$

Combine 15x and -10x to get 5x.

$$5x-5+10=4\left(x-2\right)-20$$

Add -5 and 10 to get 5.

$$5x+5=4\left(x-2\right)-20$$

Use the distributive property to multiply 4 by x-2.

$$5x+5=4x-8-20$$

Subtract 20 from -8 to get -28.

$$5x+5=4x-28$$

Subtract 4x from both sides.

$$5x+5-4x=-28$$

Combine 5x and -4x to get x.

$$x+5=-28$$

Subtract 5 from both sides.

$$x=-28-5$$

Subtract 5 from -28 to get -33.

$$x=-33$$

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

$$y=3-2\left(-33\right)-3-33$$

Multiply -2 and -33 to get 66.

$$y=3+66-3-33$$

Add 3 and 66 to get 69.

$$y=69-3-33$$

Subtract 3 from 69 to get 66.

$$y=66-33$$

Subtract 33 from 66 to get 33.

$$y=33$$

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

$$z=33$$

The system is now solved.

$$x=-33 y=33 z=33$$