Solve (x-4)/(-3x+1)=14/y

$$\frac { ( x - 4 ) } { ( - 3 x + 1 ) } = \frac { 14 } { y }$$

Solve for x

$$x=\frac{2\left(2y+7\right)}{y+42}$$

$$y\neq 0\text{ and }y\neq -42$$

Steps for Solving Linear Equation

Variable x cannot be equal to \frac{1}{3} since division by zero is not defined. Multiply both sides of the equation by y\left(3x-1\right), the least common multiple of -3x+1,y.

$$-y\left(x-4\right)=\left(3x-1\right)\times 14$$

Use the distributive property to multiply -y by x-4.

$$-yx+4y=\left(3x-1\right)\times 14$$

Use the distributive property to multiply 3x-1 by 14.

$$-yx+4y=42x-14$$

Subtract 42x from both sides.

$$-yx+4y-42x=-14$$

Subtract 4y from both sides.

$$-yx-42x=-14-4y$$

Combine all terms containing x.

$$\left(-y-42\right)x=-14-4y$$

The equation is in standard form.

$$\left(-y-42\right)x=-4y-14$$

Divide both sides by -y-42.

$$\frac{\left(-y-42\right)x}{-y-42}=\frac{-4y-14}{-y-42}$$

Dividing by -y-42 undoes the multiplication by -y-42.

$$x=\frac{-4y-14}{-y-42}$$

Divide -4y-14 by -y-42.

$$x=\frac{2\left(2y+7\right)}{y+42}$$

Variable x cannot be equal to \frac{1}{3}.

$$x=\frac{2\left(2y+7\right)}{y+42}\text{, }x\neq \frac{1}{3}$$

Solve for y

$$y=-\frac{14\left(3x-1\right)}{x-4}$$

$$x\neq \frac{1}{3}\text{ and }x\neq 4$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by y\left(3x-1\right), the least common multiple of -3x+1,y.

$$-y\left(x-4\right)=\left(3x-1\right)\times 14$$

Use the distributive property to multiply -y by x-4.

$$-yx+4y=\left(3x-1\right)\times 14$$

Use the distributive property to multiply 3x-1 by 14.

$$-yx+4y=42x-14$$

Combine all terms containing y.

$$\left(-x+4\right)y=42x-14$$

The equation is in standard form.

$$\left(4-x\right)y=42x-14$$

Divide both sides by -x+4.

$$\frac{\left(4-x\right)y}{4-x}=\frac{42x-14}{4-x}$$

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

$$y=\frac{42x-14}{4-x}$$

Divide 42x-14 by -x+4.

$$y=\frac{14\left(3x-1\right)}{4-x}$$

Variable y cannot be equal to 0.

$$y=\frac{14\left(3x-1\right)}{4-x}\text{, }y\neq 0$$