Solve 3x+4y=4x-4ab

$$3 x + 4 y = 4 x - 4 a b$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{x-4y}{4b}\text{, }&b\neq 0\\a\in \mathrm{C}\text{, }&x=4y\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

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

Subtract 4x from both sides.

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

Combine 3x and -4x to get -x.

$$-4ab=-x+4y$$

The equation is in standard form.

$$\left(-4b\right)a=4y-x$$

Divide both sides by -4b.

$$\frac{\left(-4b\right)a}{-4b}=\frac{4y-x}{-4b}$$

Dividing by -4b undoes the multiplication by -4b.

$$a=\frac{4y-x}{-4b}$$

Divide -x+4y by -4b.

$$a=-\frac{4y-x}{4b}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=\frac{x-4y}{4a}\text{, }&a\neq 0\\b\in \mathrm{C}\text{, }&x=4y\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

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

Subtract 4x from both sides.

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

Combine 3x and -4x to get -x.

$$-4ab=-x+4y$$

The equation is in standard form.

$$\left(-4a\right)b=4y-x$$

Divide both sides by -4a.

$$\frac{\left(-4a\right)b}{-4a}=\frac{4y-x}{-4a}$$

Dividing by -4a undoes the multiplication by -4a.

$$b=\frac{4y-x}{-4a}$$

Divide -x+4y by -4a.

$$b=-\frac{4y-x}{4a}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{x-4y}{4b}\text{, }&b\neq 0\\a\in \mathrm{R}\text{, }&x=4y\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

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

Subtract 4x from both sides.

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

Combine 3x and -4x to get -x.

$$-4ab=-x+4y$$

The equation is in standard form.

$$\left(-4b\right)a=4y-x$$

Divide both sides by -4b.

$$\frac{\left(-4b\right)a}{-4b}=\frac{4y-x}{-4b}$$

Dividing by -4b undoes the multiplication by -4b.

$$a=\frac{4y-x}{-4b}$$

Divide -x+4y by -4b.

$$a=-\frac{4y-x}{4b}$$

Solve for b

$$\left\{\begin{matrix}b=\frac{x-4y}{4a}\text{, }&a\neq 0\\b\in \mathrm{R}\text{, }&x=4y\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

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

Subtract 4x from both sides.

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

Combine 3x and -4x to get -x.

$$-4ab=-x+4y$$

The equation is in standard form.

$$\left(-4a\right)b=4y-x$$

Divide both sides by -4a.

$$\frac{\left(-4a\right)b}{-4a}=\frac{4y-x}{-4a}$$

Dividing by -4a undoes the multiplication by -4a.

$$b=\frac{4y-x}{-4a}$$

Divide -x+4y by -4a.

$$b=-\frac{4y-x}{4a}$$