Solve E%=(frac{X_{2}-X_{1}}{X_{1}}-frac{Y_{2}-Y_{1}}{Y_{1}})*100%

$$E \% = ( \frac { X _ { 2 } - X _ { 1 } } { X _ { 1 } } - \frac { Y _ { 2 } - Y _ { 1 } } { Y _ { 1 } } ) \times 100 \%$$

Solve for E

$$E=\frac{100\left(X_{2}Y_{1}-X_{1}Y_{2}\right)}{X_{1}Y_{1}}$$

$$Y_{1}\neq 0\text{ and }X_{1}\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 100X_{1}Y_{1}, the least common multiple of 100,X_{1},Y_{1}.

$$X_{1}Y_{1}E=\left(\frac{X_{2}-X_{1}}{X_{1}}-\frac{Y_{2}-Y_{1}}{Y_{1}}\right)X_{1}Y_{1}\times 100$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of X_{1} and Y_{1} is X_{1}Y_{1}. Multiply \frac{X_{2}-X_{1}}{X_{1}} times \frac{Y_{1}}{Y_{1}}. Multiply \frac{Y_{2}-Y_{1}}{Y_{1}} times \frac{X_{1}}{X_{1}}.

$$X_{1}Y_{1}E=\left(\frac{\left(X_{2}-X_{1}\right)Y_{1}}{X_{1}Y_{1}}-\frac{\left(Y_{2}-Y_{1}\right)X_{1}}{X_{1}Y_{1}}\right)X_{1}Y_{1}\times 100$$

Since \frac{\left(X_{2}-X_{1}\right)Y_{1}}{X_{1}Y_{1}} and \frac{\left(Y_{2}-Y_{1}\right)X_{1}}{X_{1}Y_{1}} have the same denominator, subtract them by subtracting their numerators.

$$X_{1}Y_{1}E=\frac{\left(X_{2}-X_{1}\right)Y_{1}-\left(Y_{2}-Y_{1}\right)X_{1}}{X_{1}Y_{1}}X_{1}Y_{1}\times 100$$

Do the multiplications in \left(X_{2}-X_{1}\right)Y_{1}-\left(Y_{2}-Y_{1}\right)X_{1}.

$$X_{1}Y_{1}E=\frac{X_{2}Y_{1}-X_{1}Y_{1}-Y_{2}X_{1}+Y_{1}X_{1}}{X_{1}Y_{1}}X_{1}Y_{1}\times 100$$

Combine like terms in X_{2}Y_{1}-X_{1}Y_{1}-Y_{2}X_{1}+Y_{1}X_{1}.

$$X_{1}Y_{1}E=\frac{-Y_{2}X_{1}+X_{2}Y_{1}}{X_{1}Y_{1}}X_{1}Y_{1}\times 100$$

Express \frac{-Y_{2}X_{1}+X_{2}Y_{1}}{X_{1}Y_{1}}X_{1} as a single fraction.

$$X_{1}Y_{1}E=\frac{\left(-Y_{2}X_{1}+X_{2}Y_{1}\right)X_{1}}{X_{1}Y_{1}}Y_{1}\times 100$$

Cancel out X_{1} in both numerator and denominator.

$$X_{1}Y_{1}E=\frac{-X_{1}Y_{2}+X_{2}Y_{1}}{Y_{1}}Y_{1}\times 100$$

Express \frac{-X_{1}Y_{2}+X_{2}Y_{1}}{Y_{1}}Y_{1} as a single fraction.

$$X_{1}Y_{1}E=\frac{\left(-X_{1}Y_{2}+X_{2}Y_{1}\right)Y_{1}}{Y_{1}}\times 100$$

Cancel out Y_{1} in both numerator and denominator.

$$X_{1}Y_{1}E=\left(-X_{1}Y_{2}+X_{2}Y_{1}\right)\times 100$$

Use the distributive property to multiply -X_{1}Y_{2}+X_{2}Y_{1} by 100.

$$X_{1}Y_{1}E=-100Y_{2}X_{1}+100X_{2}Y_{1}$$

The equation is in standard form.

$$X_{1}Y_{1}E=100X_{2}Y_{1}-100X_{1}Y_{2}$$

Divide both sides by Y_{1}X_{1}.

$$\frac{X_{1}Y_{1}E}{X_{1}Y_{1}}=\frac{100X_{2}Y_{1}-100X_{1}Y_{2}}{X_{1}Y_{1}}$$

Dividing by Y_{1}X_{1} undoes the multiplication by Y_{1}X_{1}.

$$E=\frac{100X_{2}Y_{1}-100X_{1}Y_{2}}{X_{1}Y_{1}}$$

Divide -100Y_{2}X_{1}+100X_{2}Y_{1} by Y_{1}X_{1}.

$$E=\frac{100X_{2}}{X_{1}}-\frac{100Y_{2}}{Y_{1}}$$

Solve for X_1

$$\left\{\begin{matrix}X_{1}=\frac{100X_{2}Y_{1}}{EY_{1}+100Y_{2}}\text{, }&Y_{1}\neq 0\text{ and }X_{2}\neq 0\text{ and }E\neq -\frac{100Y_{2}}{Y_{1}}\text{ and }Y_{2}\neq -\frac{EY_{1}}{100}\\X_{1}\neq 0\text{, }&X_{2}=0\text{ and }Y_{2}=-\frac{EY_{1}}{100}\text{ and }Y_{1}\neq 0\end{matrix}\right.$$