Solve 1/4x-1/5y=-1

$$\frac{ 1 }{ 4 } x- \frac{ 1 }{ 5 } y = -1$$

Solve for x

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

Steps for Solving Linear Equation

Add \frac{1}{5}y to both sides.

$$\frac{1}{4}x=-1+\frac{1}{5}y$$

The equation is in standard form.

$$\frac{1}{4}x=\frac{y}{5}-1$$

Multiply both sides by 4.

$$\frac{\frac{1}{4}x}{\frac{1}{4}}=\frac{\frac{y}{5}-1}{\frac{1}{4}}$$

Dividing by \frac{1}{4} undoes the multiplication by \frac{1}{4}.

$$x=\frac{\frac{y}{5}-1}{\frac{1}{4}}$$

Divide -1+\frac{y}{5} by \frac{1}{4} by multiplying -1+\frac{y}{5} by the reciprocal of \frac{1}{4}.

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

Solve for y

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

Steps for Solving Linear Equation

Subtract \frac{1}{4}x from both sides.

$$-\frac{1}{5}y=-1-\frac{1}{4}x$$

The equation is in standard form.

$$-\frac{1}{5}y=-\frac{x}{4}-1$$

Multiply both sides by -5.

$$\frac{-\frac{1}{5}y}{-\frac{1}{5}}=\frac{-\frac{x}{4}-1}{-\frac{1}{5}}$$

Dividing by -\frac{1}{5} undoes the multiplication by -\frac{1}{5}.

$$y=\frac{-\frac{x}{4}-1}{-\frac{1}{5}}$$

Divide -1-\frac{x}{4} by -\frac{1}{5} by multiplying -1-\frac{x}{4} by the reciprocal of -\frac{1}{5}.

$$y=\frac{5x}{4}+5$$