Solve x/24:x/66y=3:4

$$\frac { x } { 24 } : \frac { x } { 66 y } = 3 : 4$$

Solve for x

$$x\neq 0$$

$$x\neq 0\text{ and }y=\frac{3}{11}$$

Steps for Solving Linear Equation

Divide \frac{x}{24} by \frac{x}{66y} by multiplying \frac{x}{24} by the reciprocal of \frac{x}{66y}.

$$\frac{x\times 66y}{24x}=\frac{3}{4}$$

Cancel out 6 in both numerator and denominator.

$$\frac{11xy}{4x}=\frac{3}{4}$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4x, the least common multiple of 4x,4.

$$11xy=3x$$

Subtract 3x from both sides.

$$11xy-3x=0$$

Combine all terms containing x.

$$\left(11y-3\right)x=0$$

Divide 0 by 11y-3.

$$x=0$$

Variable x cannot be equal to 0.

$$x\in \emptyset$$

Solve for y

$$y = \frac{3}{11} = 0.2727272727272727$$

$$x\neq 0$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Divide \frac{x}{24} by \frac{x}{66y} by multiplying \frac{x}{24} by the reciprocal of \frac{x}{66y}.

$$\frac{x\times 66y}{24x}=\frac{3}{4}$$

Cancel out 6x in both numerator and denominator.

$$\frac{11y}{4}=\frac{3}{4}$$

Multiply both sides by 4.

$$11y=\frac{3}{4}\times 4$$

Multiply \frac{3}{4} and 4 to get 3.

$$11y=3$$

Divide both sides by 11.

$$y=\frac{3}{11}$$