Solve 1/4x-1/6y=-1

$$\frac { 1 } { 4 } x - \frac { 1 } { 6 } y = - 1$$

Solve for x

$$x=\frac{2\left(y-6\right)}{3}$$

Steps for Solving Linear Equation

Add \frac{1}{6}y to both sides.

$$\frac{1}{4}x=-1+\frac{1}{6}y$$

The equation is in standard form.

$$\frac{1}{4}x=\frac{y}{6}-1$$

Multiply both sides by 4.

$$\frac{\frac{1}{4}x}{\frac{1}{4}}=\frac{\frac{y}{6}-1}{\frac{1}{4}}$$

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

$$x=\frac{\frac{y}{6}-1}{\frac{1}{4}}$$

Divide -1+\frac{y}{6} by \frac{1}{4} by multiplying -1+\frac{y}{6} by the reciprocal of \frac{1}{4}.

$$x=\frac{2y}{3}-4$$

Solve for y

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

Steps for Solving Linear Equation

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

$$-\frac{1}{6}y=-1-\frac{1}{4}x$$

The equation is in standard form.

$$-\frac{1}{6}y=-\frac{x}{4}-1$$

Multiply both sides by -6.

$$\frac{-\frac{1}{6}y}{-\frac{1}{6}}=\frac{-\frac{x}{4}-1}{-\frac{1}{6}}$$

Dividing by -\frac{1}{6} undoes the multiplication by -\frac{1}{6}.

$$y=\frac{-\frac{x}{4}-1}{-\frac{1}{6}}$$

Divide -1-\frac{x}{4} by -\frac{1}{6} by multiplying -1-\frac{x}{4} by the reciprocal of -\frac{1}{6}.

$$y=\frac{3x}{2}+6$$