Solve 6xy+4x-9y-7=22

$$6xy+4x-9y-7=22$$

Solve for x

$$x=\frac{9y+29}{2\left(3y+2\right)}$$

$$y\neq -\frac{2}{3}$$

Steps for Solving Linear Equation

Add 9y to both sides.

$$6xy+4x-7=22+9y$$

Add 7 to both sides.

$$6xy+4x=22+9y+7$$

Add 22 and 7 to get 29.

$$6xy+4x=29+9y$$

Combine all terms containing x.

$$\left(6y+4\right)x=29+9y$$

The equation is in standard form.

$$\left(6y+4\right)x=9y+29$$

Divide both sides by 6y+4.

$$\frac{\left(6y+4\right)x}{6y+4}=\frac{9y+29}{6y+4}$$

Dividing by 6y+4 undoes the multiplication by 6y+4.

$$x=\frac{9y+29}{6y+4}$$

Divide 29+9y by 6y+4.

$$x=\frac{9y+29}{2\left(3y+2\right)}$$

Solve for y

$$y=-\frac{4x-29}{3\left(2x-3\right)}$$

$$x\neq \frac{3}{2}$$

Steps for Solving Linear Equation

Subtract 4x from both sides.

$$6xy-9y-7=22-4x$$

Add 7 to both sides.

$$6xy-9y=22-4x+7$$

Add 22 and 7 to get 29.

$$6xy-9y=29-4x$$

Combine all terms containing y.

$$\left(6x-9\right)y=29-4x$$

Divide both sides by 6x-9.

$$\frac{\left(6x-9\right)y}{6x-9}=\frac{29-4x}{6x-9}$$

Dividing by 6x-9 undoes the multiplication by 6x-9.

$$y=\frac{29-4x}{6x-9}$$

Divide 29-4x by 6x-9.

$$y=\frac{29-4x}{3\left(2x-3\right)}$$