Solve 1:y=-1/4x-3

$$1 : y = - \frac { 1 } { 4 } x - 3$$

Solve for x

$$x=-12-\frac{4}{y}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4y, the least common multiple of y,4.

$$4=-\frac{1}{4}x\times 4y+4y\left(-3\right)$$

Multiply -\frac{1}{4} and 4 to get -1.

$$4=-xy+4y\left(-3\right)$$

Multiply 4 and -3 to get -12.

$$4=-xy-12y$$

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

$$-xy-12y=4$$

Add 12y to both sides.

$$-xy=4+12y$$

The equation is in standard form.

$$\left(-y\right)x=12y+4$$

Divide both sides by -y.

$$\frac{\left(-y\right)x}{-y}=\frac{12y+4}{-y}$$

Dividing by -y undoes the multiplication by -y.

$$x=\frac{12y+4}{-y}$$

Divide 4+12y by -y.

$$x=-12-\frac{4}{y}$$

Solve for y

$$y=-\frac{4}{x+12}$$

$$x\neq -12$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4y, the least common multiple of y,4.

$$4=-\frac{1}{4}x\times 4y+4y\left(-3\right)$$

Multiply -\frac{1}{4} and 4 to get -1.

$$4=-xy+4y\left(-3\right)$$

Multiply 4 and -3 to get -12.

$$4=-xy-12y$$

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

$$-xy-12y=4$$

Combine all terms containing y.

$$\left(-x-12\right)y=4$$

Divide both sides by -x-12.

$$\frac{\left(-x-12\right)y}{-x-12}=\frac{4}{-x-12}$$

Dividing by -x-12 undoes the multiplication by -x-12.

$$y=\frac{4}{-x-12}$$

Divide 4 by -x-12.

$$y=-\frac{4}{x+12}$$

Variable y cannot be equal to 0.

$$y=-\frac{4}{x+12}\text{, }y\neq 0$$