Solve [3.5Y_{3}+(-9Y_{3})-25Y]-(+2XY-3Y_{3}-5Y)=-2,038.5D_{0}

$$[ 3.5 Y _ { 3 } + ( - 9 Y _ { 3 } ) - 25 Y ] - ( + 2 X Y - 3 Y _ { 3 } - 5 Y ) = - 2,038.5 D _ { 0 }$$

Solve for D_0

$$D_{0}=\frac{4XY+40Y+5Y_{3}}{4077}$$

Steps for Solving Linear Equation

Combine 3.5Y_{3} and -9Y_{3} to get -5.5Y_{3}.

$$-5.5Y_{3}-25Y-\left(2XY-3Y_{3}-5Y\right)=-2038.5D_{0}$$

To find the opposite of 2XY-3Y_{3}-5Y, find the opposite of each term.

$$-5.5Y_{3}-25Y-2XY+3Y_{3}+5Y=-2038.5D_{0}$$

Combine -5.5Y_{3} and 3Y_{3} to get -2.5Y_{3}.

$$-2.5Y_{3}-25Y-2XY+5Y=-2038.5D_{0}$$

Combine -25Y and 5Y to get -20Y.

$$-2.5Y_{3}-20Y-2XY=-2038.5D_{0}$$

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

$$-2038.5D_{0}=-2.5Y_{3}-20Y-2XY$$

The equation is in standard form.

$$-2038.5D_{0}=-2XY-\frac{5Y_{3}}{2}-20Y$$

Divide both sides of the equation by -2038.5, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-2038.5D_{0}}{-2038.5}=\frac{-2XY-\frac{5Y_{3}}{2}-20Y}{-2038.5}$$

Dividing by -2038.5 undoes the multiplication by -2038.5.

$$D_{0}=\frac{-2XY-\frac{5Y_{3}}{2}-20Y}{-2038.5}$$

Divide -\frac{5Y_{3}}{2}-20Y-2XY by -2038.5 by multiplying -\frac{5Y_{3}}{2}-20Y-2XY by the reciprocal of -2038.5.

$$D_{0}=\frac{4XY+40Y+5Y_{3}}{4077}$$

Solve for X

$$\left\{\begin{matrix}X=-\frac{\frac{5Y_{3}}{2}-\frac{4077D_{0}}{2}+20Y}{2Y}\text{, }&Y\neq 0\\X\in \mathrm{R}\text{, }&Y_{3}=\frac{4077D_{0}}{5}\text{ and }Y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine 3.5Y_{3} and -9Y_{3} to get -5.5Y_{3}.

$$-5.5Y_{3}-25Y-\left(2XY-3Y_{3}-5Y\right)=-2038.5D_{0}$$

To find the opposite of 2XY-3Y_{3}-5Y, find the opposite of each term.

$$-5.5Y_{3}-25Y-2XY+3Y_{3}+5Y=-2038.5D_{0}$$

Combine -5.5Y_{3} and 3Y_{3} to get -2.5Y_{3}.

$$-2.5Y_{3}-25Y-2XY+5Y=-2038.5D_{0}$$

Combine -25Y and 5Y to get -20Y.

$$-2.5Y_{3}-20Y-2XY=-2038.5D_{0}$$

Add 2.5Y_{3} to both sides.

$$-20Y-2XY=-2038.5D_{0}+2.5Y_{3}$$

Add 20Y to both sides.

$$-2XY=-2038.5D_{0}+2.5Y_{3}+20Y$$

The equation is in standard form.

$$\left(-2Y\right)X=\frac{5Y_{3}}{2}-\frac{4077D_{0}}{2}+20Y$$

Divide both sides by -2Y.

$$\frac{\left(-2Y\right)X}{-2Y}=\frac{\frac{5Y_{3}}{2}-\frac{4077D_{0}}{2}+20Y}{-2Y}$$

Dividing by -2Y undoes the multiplication by -2Y.

$$X=\frac{\frac{5Y_{3}}{2}-\frac{4077D_{0}}{2}+20Y}{-2Y}$$

Divide -\frac{4077D_{0}}{2}+\frac{5Y_{3}}{2}+20Y by -2Y.

$$X=-\frac{5Y_{3}+40Y-4077D_{0}}{4Y}$$