Solve [35Y_{3}+(-9Y_{3})-25Y]-(+2XY-3Y_{3}-5Y)=-2.0385D_{0}

$$[ 35 Y _ { 3 } + ( - 9 Y _ { 3 } ) - 25 Y ] - ( + 2 X Y - 3 Y _ { 3 } - 5 Y ) = - 2.0385 D _ { 0 }$$

Solve for D_0

$$D_{0}=\frac{4000XY+40000Y-58000Y_{3}}{4077}$$

Steps for Solving Linear Equation

Combine 35Y_{3} and -9Y_{3} to get 26Y_{3}.

$$26Y_{3}-25Y-\left(2XY-3Y_{3}-5Y\right)=-2.0385D_{0}$$

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

$$26Y_{3}-25Y-2XY+3Y_{3}+5Y=-2.0385D_{0}$$

Combine 26Y_{3} and 3Y_{3} to get 29Y_{3}.

$$29Y_{3}-25Y-2XY+5Y=-2.0385D_{0}$$

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

$$29Y_{3}-20Y-2XY=-2.0385D_{0}$$

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

$$-2.0385D_{0}=29Y_{3}-20Y-2XY$$

Divide both sides of the equation by -2.0385, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-2.0385D_{0}}{-2.0385}=\frac{29Y_{3}-20Y-2XY}{-2.0385}$$

Dividing by -2.0385 undoes the multiplication by -2.0385.

$$D_{0}=\frac{29Y_{3}-20Y-2XY}{-2.0385}$$

Divide 29Y_{3}-20Y-2XY by -2.0385 by multiplying 29Y_{3}-20Y-2XY by the reciprocal of -2.0385.

$$D_{0}=\frac{4000XY+40000Y-58000Y_{3}}{4077}$$

Solve for X

$$\left\{\begin{matrix}X=\frac{4077D_{0}-40000Y+58000Y_{3}}{4000Y}\text{, }&Y\neq 0\\X\in \mathrm{R}\text{, }&Y_{3}=-\frac{4077D_{0}}{58000}\text{ and }Y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine 35Y_{3} and -9Y_{3} to get 26Y_{3}.

$$26Y_{3}-25Y-\left(2XY-3Y_{3}-5Y\right)=-2.0385D_{0}$$

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

$$26Y_{3}-25Y-2XY+3Y_{3}+5Y=-2.0385D_{0}$$

Combine 26Y_{3} and 3Y_{3} to get 29Y_{3}.

$$29Y_{3}-25Y-2XY+5Y=-2.0385D_{0}$$

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

$$29Y_{3}-20Y-2XY=-2.0385D_{0}$$

Subtract 29Y_{3} from both sides.

$$-20Y-2XY=-2.0385D_{0}-29Y_{3}$$

Add 20Y to both sides.

$$-2XY=-2.0385D_{0}-29Y_{3}+20Y$$

The equation is in standard form.

$$\left(-2Y\right)X=-\frac{4077D_{0}}{2000}+20Y-29Y_{3}$$

Divide both sides by -2Y.

$$\frac{\left(-2Y\right)X}{-2Y}=\frac{-\frac{4077D_{0}}{2000}+20Y-29Y_{3}}{-2Y}$$

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

$$X=\frac{-\frac{4077D_{0}}{2000}+20Y-29Y_{3}}{-2Y}$$

Divide -29Y_{3}-\frac{4077D_{0}}{2000}+20Y by -2Y.

$$X=\frac{\frac{29Y_{3}}{2}+\frac{4077D_{0}}{4000}}{Y}-10$$