Solve {l}{x-1/2=y-2/3=z-3/4}{text{ind}x-4/5=frac{y-1}{2}=z}

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

Solve for x

$$x=\frac{2y-1}{3}$$

Steps for Solving Linear Equation

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

$$3\left(x-1\right)=2\left(y-2\right)$$

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

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

Use the distributive property to multiply 2 by y-2.

$$3x-3=2y-4$$

Add 3 to both sides.

$$3x=2y-4+3$$

Add -4 and 3 to get -1.

$$3x=2y-1$$

Divide both sides by 3.

$$\frac{3x}{3}=\frac{2y-1}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x=\frac{2y-1}{3}$$