Solve {l}{x+2/3=2y+3/4=3z+4/5}{4x+12y-3z+1=0}

$$\left. \begin{array} { l } { \frac { x + 2 } { 3 } = \frac { 2 y + 3 } { 4 } = \frac { 3 z + 4 } { 5 } } \\ { 4 x + 12 y - 3 z + 1 = 0 } \end{array} \right.$$

Solve for x

$$x=\frac{3y}{2}+\frac{1}{4}$$

Steps for Solving Linear Equation

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

$$4\left(x+2\right)=3\left(2y+3\right)$$

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

$$4x+8=3\left(2y+3\right)$$

Use the distributive property to multiply 3 by 2y+3.

$$4x+8=6y+9$$

Subtract 8 from both sides.

$$4x=6y+9-8$$

Subtract 8 from 9 to get 1.

$$4x=6y+1$$

Divide both sides by 4.

$$\frac{4x}{4}=\frac{6y+1}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x=\frac{6y+1}{4}$$

Divide 6y+1 by 4.

$$x=\frac{3y}{2}+\frac{1}{4}$$