Solve x=-1/y-1+3/4

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

Solve for y

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

$$x\neq \frac{3}{4}$$

Steps for Solving Linear Equation

Variable y cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by 4\left(y-1\right), the least common multiple of y-1,4.

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

Use the distributive property to multiply x\times 4 by y-1.

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

Multiply -1 and 4 to get -4.

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

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

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

Use the distributive property to multiply 3 by y-1.

$$4xy-4x=-4+3y-3$$

Subtract 3 from -4 to get -7.

$$4xy-4x=-7+3y$$

Subtract 3y from both sides.

$$4xy-4x-3y=-7$$

Add 4x to both sides.

$$4xy-3y=-7+4x$$

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by 4x-3.

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

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

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

Variable y cannot be equal to 1.

$$y=\frac{4x-7}{4x-3}\text{, }y\neq 1$$

Solve for x

$$x=-\frac{7-3y}{4\left(y-1\right)}$$

$$y\neq 1$$