Solve 4x-yx-5y=2yx+16

$$4x-yx-5y=2yx+16$$

Solve for x

$$x=\frac{5y+16}{4-3y}$$

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

Steps for Solving Linear Equation

Subtract 2yx from both sides.

$$4x-yx-5y-2yx=16$$

Combine -yx and -2yx to get -3yx.

$$4x-3yx-5y=16$$

Add 5y to both sides.

$$4x-3yx=16+5y$$

Combine all terms containing x.

$$\left(4-3y\right)x=16+5y$$

The equation is in standard form.

$$\left(4-3y\right)x=5y+16$$

Divide both sides by -3y+4.

$$\frac{\left(4-3y\right)x}{4-3y}=\frac{5y+16}{4-3y}$$

Dividing by -3y+4 undoes the multiplication by -3y+4.

$$x=\frac{5y+16}{4-3y}$$

Solve for y

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

$$x\neq -\frac{5}{3}$$

Steps for Solving Linear Equation

Subtract 2yx from both sides.

$$4x-yx-5y-2yx=16$$

Combine -yx and -2yx to get -3yx.

$$4x-3yx-5y=16$$

Subtract 4x from both sides.

$$-3yx-5y=16-4x$$

Combine all terms containing y.

$$\left(-3x-5\right)y=16-4x$$

Divide both sides by -3x-5.

$$\frac{\left(-3x-5\right)y}{-3x-5}=\frac{16-4x}{-3x-5}$$

Dividing by -3x-5 undoes the multiplication by -3x-5.

$$y=\frac{16-4x}{-3x-5}$$

Divide 16-4x by -3x-5.

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