Solve (1-3y)/x-4y=-24

$$\frac { ( 1 - 3 y ) } { x } - 4 y = - 24$$

Solve for x

$$x=-\frac{1-3y}{4\left(6-y\right)}$$

$$y\neq \frac{1}{3}\text{ and }y\neq 6$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$1-3y-4yx=-24x$$

Add 24x to both sides.

$$1-3y-4yx+24x=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$-3y-4yx+24x=-1$$

Add 3y to both sides.

$$-4yx+24x=-1+3y$$

Combine all terms containing x.

$$\left(-4y+24\right)x=-1+3y$$

The equation is in standard form.

$$\left(24-4y\right)x=3y-1$$

Divide both sides by -4y+24.

$$\frac{\left(24-4y\right)x}{24-4y}=\frac{3y-1}{24-4y}$$

Dividing by -4y+24 undoes the multiplication by -4y+24.

$$x=\frac{3y-1}{24-4y}$$

Divide -1+3y by -4y+24.

$$x=\frac{3y-1}{4\left(6-y\right)}$$

Variable x cannot be equal to 0.

$$x=\frac{3y-1}{4\left(6-y\right)}\text{, }x\neq 0$$

Solve for y

$$y=\frac{24x+1}{4x+3}$$

$$x\neq -\frac{3}{4}\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$1-3y-4yx=-24x$$

Subtract 1 from both sides.

$$-3y-4yx=-24x-1$$

Combine all terms containing y.

$$\left(-3-4x\right)y=-24x-1$$

The equation is in standard form.

$$\left(-4x-3\right)y=-24x-1$$

Divide both sides by -3-4x.

$$\frac{\left(-4x-3\right)y}{-4x-3}=\frac{-24x-1}{-4x-3}$$

Dividing by -3-4x undoes the multiplication by -3-4x.

$$y=\frac{-24x-1}{-4x-3}$$

Divide -24x-1 by -3-4x.

$$y=\frac{24x+1}{4x+3}$$