Solve {l}{x/3a+4b=y/6b+c=z/2c-9a}{2y+z=}

$$\left. \begin{array} { l } { \frac { x } { 3 a + 4 b } = \frac { y } { 6 b + c } = \frac { z } { 2 c - 9 a } } \\ { 2 y + z = } \end{array} \right.$$

Solve for x

$$x=\frac{y\left(3a+4b\right)}{c+6b}$$

$$a\neq -\frac{4b}{3}\text{ and }b\neq -\frac{c}{6}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(6b+c\right)\left(3a+4b\right), the least common multiple of 3a+4b,6b+c.

$$\left(6b+c\right)x=\left(3a+4b\right)y$$

Use the distributive property to multiply 6b+c by x.

$$6bx+cx=\left(3a+4b\right)y$$

Use the distributive property to multiply 3a+4b by y.

$$6bx+cx=3ay+4by$$

Combine all terms containing x.

$$\left(6b+c\right)x=3ay+4by$$

Divide both sides by 6b+c.

$$\frac{\left(6b+c\right)x}{6b+c}=\frac{y\left(3a+4b\right)}{6b+c}$$

Dividing by 6b+c undoes the multiplication by 6b+c.

$$x=\frac{y\left(3a+4b\right)}{6b+c}$$

Divide y\left(3a+4b\right) by 6b+c.

$$x=\frac{y\left(3a+4b\right)}{c+6b}$$