Solve x/1-p+y/1+1=1+3i

$$\frac { x } { 1 - p } + \frac { y } { 1 + 1 } = 1 + 3 i$$

Solve for p

$$\left\{\begin{matrix}p=-\frac{2x+y+\left(-2-6i\right)}{2+6i-y}\text{, }&x\neq 0\text{ and }y\neq 2+6i\\p\neq 1\text{, }&y=2+6i\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable p cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by -p+1.

$$x+\left(-\frac{1}{2}p+\frac{1}{2}\right)y=\left(1+3i\right)\left(-p+1\right)$$

Use the distributive property to multiply -\frac{1}{2}p+\frac{1}{2} by y.

$$x-\frac{1}{2}py+\frac{1}{2}y=\left(1+3i\right)\left(-p+1\right)$$

Use the distributive property to multiply 1+3i by -p+1.

$$x-\frac{1}{2}py+\frac{1}{2}y=\left(-1-3i\right)p+\left(1+3i\right)$$

Subtract \left(-1-3i\right)p from both sides.

$$x-\frac{1}{2}py+\frac{1}{2}y-\left(-1-3i\right)p=1+3i$$

Multiply -1 and -1-3i to get 1+3i.

$$x-\frac{1}{2}py+\frac{1}{2}y+\left(1+3i\right)p=1+3i$$

Subtract x from both sides.

$$-\frac{1}{2}py+\frac{1}{2}y+\left(1+3i\right)p=1+3i-x$$

Subtract \frac{1}{2}y from both sides.

$$-\frac{1}{2}py+\left(1+3i\right)p=1+3i-x-\frac{1}{2}y$$

Combine all terms containing p.

$$\left(-\frac{1}{2}y+\left(1+3i\right)\right)p=1+3i-x-\frac{1}{2}y$$

The equation is in standard form.

$$\left(-\frac{y}{2}+\left(1+3i\right)\right)p=-\frac{y}{2}-x+\left(1+3i\right)$$

Divide both sides by -\frac{1}{2}y+\left(1+3i\right).

$$\frac{\left(-\frac{y}{2}+\left(1+3i\right)\right)p}{-\frac{y}{2}+\left(1+3i\right)}=\frac{-\frac{y}{2}-x+\left(1+3i\right)}{-\frac{y}{2}+\left(1+3i\right)}$$

Dividing by -\frac{1}{2}y+\left(1+3i\right) undoes the multiplication by -\frac{1}{2}y+\left(1+3i\right).

$$p=\frac{-\frac{y}{2}-x+\left(1+3i\right)}{-\frac{y}{2}+\left(1+3i\right)}$$

Divide 1+3i-x-\frac{y}{2} by -\frac{1}{2}y+\left(1+3i\right).

$$p=\frac{2+6i-y-2x}{2+6i-y}$$

Variable p cannot be equal to 1.

$$p=\frac{2+6i-y-2x}{2+6i-y}\text{, }p\neq 1$$

Solve for x

$$x=\frac{py-y+\left(-2-6i\right)p+\left(2+6i\right)}{2}$$

$$p\neq 1$$

Solution Steps

Multiply both sides of the equation by -p+1.

$$x+\left(-\frac{1}{2}p+\frac{1}{2}\right)y=\left(1+3i\right)\left(-p+1\right)$$

Use the distributive property to multiply -\frac{1}{2}p+\frac{1}{2} by y.

$$x-\frac{1}{2}py+\frac{1}{2}y=\left(1+3i\right)\left(-p+1\right)$$

Use the distributive property to multiply 1+3i by -p+1.

$$x-\frac{1}{2}py+\frac{1}{2}y=\left(-1-3i\right)p+\left(1+3i\right)$$

Add \frac{1}{2}py to both sides.

$$x+\frac{1}{2}y=\left(-1-3i\right)p+\left(1+3i\right)+\frac{1}{2}py$$

Subtract \frac{1}{2}y from both sides.

$$x=\left(-1-3i\right)p+\left(1+3i\right)+\frac{1}{2}py-\frac{1}{2}y$$