Solve 12x+46xy=65y-1

$$12x+46xy=65y-1$$

Solve for x

$$x=-\frac{1-65y}{2\left(23y+6\right)}$$

$$y\neq -\frac{6}{23}$$

Steps for Solving Linear Equation

Combine all terms containing x.

$$\left(12+46y\right)x=65y-1$$

The equation is in standard form.

$$\left(46y+12\right)x=65y-1$$

Divide both sides by 46y+12.

$$\frac{\left(46y+12\right)x}{46y+12}=\frac{65y-1}{46y+12}$$

Dividing by 46y+12 undoes the multiplication by 46y+12.

$$x=\frac{65y-1}{46y+12}$$

Divide 65y-1 by 46y+12.

$$x=\frac{65y-1}{2\left(23y+6\right)}$$

Solve for y

$$y=-\frac{12x+1}{46x-65}$$

$$x\neq \frac{65}{46}$$

Steps for Solving Linear Equation

Subtract 65y from both sides.

$$12x+46xy-65y=-1$$

Subtract 12x from both sides.

$$46xy-65y=-1-12x$$

Combine all terms containing y.

$$\left(46x-65\right)y=-1-12x$$

The equation is in standard form.

$$\left(46x-65\right)y=-12x-1$$

Divide both sides by 46x-65.

$$\frac{\left(46x-65\right)y}{46x-65}=\frac{-12x-1}{46x-65}$$

Dividing by 46x-65 undoes the multiplication by 46x-65.

$$y=\frac{-12x-1}{46x-65}$$

Divide -1-12x by 46x-65.

$$y=-\frac{12x+1}{46x-65}$$