Solve y=4-5x/6-7x

$$y = \frac { 4 - 5 x } { 6 - 7 x }$$

Solve for x

$$x=-\frac{2\left(3y-2\right)}{5-7y}$$

$$y\neq \frac{5}{7}$$

Steps for Solving Linear Equation

Variable x cannot be equal to \frac{6}{7} since division by zero is not defined. Multiply both sides of the equation by -7x+6.

$$y\left(-7x+6\right)=4-5x$$

Use the distributive property to multiply y by -7x+6.

$$-7yx+6y=4-5x$$

Add 5x to both sides.

$$-7yx+6y+5x=4$$

Subtract 6y from both sides.

$$-7yx+5x=4-6y$$

Combine all terms containing x.

$$\left(-7y+5\right)x=4-6y$$

The equation is in standard form.

$$\left(5-7y\right)x=4-6y$$

Divide both sides by -7y+5.

$$\frac{\left(5-7y\right)x}{5-7y}=\frac{4-6y}{5-7y}$$

Dividing by -7y+5 undoes the multiplication by -7y+5.

$$x=\frac{4-6y}{5-7y}$$

Divide 4-6y by -7y+5.

$$x=\frac{2\left(2-3y\right)}{5-7y}$$

Variable x cannot be equal to \frac{6}{7}.

$$x=\frac{2\left(2-3y\right)}{5-7y}\text{, }x\neq \frac{6}{7}$$

Solve for y

$$y=-\frac{5x-4}{6-7x}$$

$$x\neq \frac{6}{7}$$