Solve f3x-5y/7x-4y=3/4

$$f \frac { 3 x - 5 y } { 7 x - 4 y } = \frac { 3 } { 4 }$$

Solve for f

$$f=-\frac{3\left(4y-7x\right)}{4\left(3x-5y\right)}$$

$$x\neq \frac{5y}{3}\text{ and }x\neq \frac{4y}{7}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4\left(-7x+4y\right), the least common multiple of 7x-4y,4.

$$f\left(-4\right)\left(3x-5y\right)=3\left(-7x+4y\right)$$

Use the distributive property to multiply f\left(-4\right) by 3x-5y.

$$-12fx+20fy=3\left(-7x+4y\right)$$

Use the distributive property to multiply 3 by -7x+4y.

$$-12fx+20fy=-21x+12y$$

Combine all terms containing f.

$$\left(-12x+20y\right)f=-21x+12y$$

The equation is in standard form.

$$\left(20y-12x\right)f=12y-21x$$

Divide both sides by -12x+20y.

$$\frac{\left(20y-12x\right)f}{20y-12x}=\frac{12y-21x}{20y-12x}$$

Dividing by -12x+20y undoes the multiplication by -12x+20y.

$$f=\frac{12y-21x}{20y-12x}$$

Divide -21x+12y by -12x+20y.

$$f=\frac{3\left(4y-7x\right)}{4\left(5y-3x\right)}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{4y\left(3-5f\right)}{3\left(4f-7\right)}\text{, }&f\neq 0\text{ and }y\neq 0\text{ and }f\neq \frac{7}{4}\\x\neq 0\text{, }&y=0\text{ and }f=\frac{7}{4}\end{matrix}\right.$$