Solve 13/22b-1/4xy+3/2xy-1/2ab=0

$$\frac { 13 } { 2 } 2 b - \frac { 1 } { 4 } x y + \frac { 3 } { 2 } x y - \frac { 1 } { 2 } a b = 0$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{5xy}{2b}+26\text{, }&b\neq 0\\a\in \mathrm{C}\text{, }&\left(x=0\text{ or }y=0\right)\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply \frac{13}{2} and 2 to get 13.

$$13b-\frac{1}{4}xy+\frac{3}{2}xy-\frac{1}{2}ab=0$$

Combine -\frac{1}{4}xy and \frac{3}{2}xy to get \frac{5}{4}xy.

$$13b+\frac{5}{4}xy-\frac{1}{2}ab=0$$

Subtract 13b from both sides. Anything subtracted from zero gives its negation.

$$\frac{5}{4}xy-\frac{1}{2}ab=-13b$$

Subtract \frac{5}{4}xy from both sides.

$$-\frac{1}{2}ab=-13b-\frac{5}{4}xy$$

The equation is in standard form.

$$\left(-\frac{b}{2}\right)a=-\frac{5xy}{4}-13b$$

Divide both sides by -\frac{1}{2}b.

$$\frac{\left(-\frac{b}{2}\right)a}{-\frac{b}{2}}=\frac{-\frac{5xy}{4}-13b}{-\frac{b}{2}}$$

Dividing by -\frac{1}{2}b undoes the multiplication by -\frac{1}{2}b.

$$a=\frac{-\frac{5xy}{4}-13b}{-\frac{b}{2}}$$

Divide -13b-\frac{5xy}{4} by -\frac{1}{2}b.

$$a=\frac{5xy}{2b}+26$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-\frac{5xy}{2\left(26-a\right)}\text{, }&a\neq 26\\b\in \mathrm{C}\text{, }&\left(x=0\text{ or }y=0\right)\text{ and }a=26\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply \frac{13}{2} and 2 to get 13.

$$13b-\frac{1}{4}xy+\frac{3}{2}xy-\frac{1}{2}ab=0$$

Combine -\frac{1}{4}xy and \frac{3}{2}xy to get \frac{5}{4}xy.

$$13b+\frac{5}{4}xy-\frac{1}{2}ab=0$$

Subtract \frac{5}{4}xy from both sides. Anything subtracted from zero gives its negation.

$$13b-\frac{1}{2}ab=-\frac{5}{4}xy$$

Combine all terms containing b.

$$\left(13-\frac{1}{2}a\right)b=-\frac{5}{4}xy$$

The equation is in standard form.

$$\left(-\frac{a}{2}+13\right)b=-\frac{5xy}{4}$$

Divide both sides by 13-\frac{1}{2}a.

$$\frac{\left(-\frac{a}{2}+13\right)b}{-\frac{a}{2}+13}=-\frac{\frac{5xy}{4}}{-\frac{a}{2}+13}$$

Dividing by 13-\frac{1}{2}a undoes the multiplication by 13-\frac{1}{2}a.

$$b=-\frac{\frac{5xy}{4}}{-\frac{a}{2}+13}$$

Divide -\frac{5xy}{4} by 13-\frac{1}{2}a.

$$b=-\frac{5xy}{2\left(26-a\right)}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{5xy}{2b}+26\text{, }&b\neq 0\\a\in \mathrm{R}\text{, }&\left(x=0\text{ or }y=0\right)\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply \frac{13}{2} and 2 to get 13.

$$13b-\frac{1}{4}xy+\frac{3}{2}xy-\frac{1}{2}ab=0$$

Combine -\frac{1}{4}xy and \frac{3}{2}xy to get \frac{5}{4}xy.

$$13b+\frac{5}{4}xy-\frac{1}{2}ab=0$$

Subtract 13b from both sides. Anything subtracted from zero gives its negation.

$$\frac{5}{4}xy-\frac{1}{2}ab=-13b$$

Subtract \frac{5}{4}xy from both sides.

$$-\frac{1}{2}ab=-13b-\frac{5}{4}xy$$

The equation is in standard form.

$$\left(-\frac{b}{2}\right)a=-\frac{5xy}{4}-13b$$

Divide both sides by -\frac{1}{2}b.

$$\frac{\left(-\frac{b}{2}\right)a}{-\frac{b}{2}}=\frac{-\frac{5xy}{4}-13b}{-\frac{b}{2}}$$

Dividing by -\frac{1}{2}b undoes the multiplication by -\frac{1}{2}b.

$$a=\frac{-\frac{5xy}{4}-13b}{-\frac{b}{2}}$$

Divide -13b-\frac{5xy}{4} by -\frac{1}{2}b.

$$a=\frac{5xy}{2b}+26$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{5xy}{2\left(26-a\right)}\text{, }&a\neq 26\\b\in \mathrm{R}\text{, }&\left(x=0\text{ or }y=0\right)\text{ and }a=26\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply \frac{13}{2} and 2 to get 13.

$$13b-\frac{1}{4}xy+\frac{3}{2}xy-\frac{1}{2}ab=0$$

Combine -\frac{1}{4}xy and \frac{3}{2}xy to get \frac{5}{4}xy.

$$13b+\frac{5}{4}xy-\frac{1}{2}ab=0$$

Subtract \frac{5}{4}xy from both sides. Anything subtracted from zero gives its negation.

$$13b-\frac{1}{2}ab=-\frac{5}{4}xy$$

Combine all terms containing b.

$$\left(13-\frac{1}{2}a\right)b=-\frac{5}{4}xy$$

The equation is in standard form.

$$\left(-\frac{a}{2}+13\right)b=-\frac{5xy}{4}$$

Divide both sides by 13-\frac{1}{2}a.

$$\frac{\left(-\frac{a}{2}+13\right)b}{-\frac{a}{2}+13}=-\frac{\frac{5xy}{4}}{-\frac{a}{2}+13}$$

Dividing by 13-\frac{1}{2}a undoes the multiplication by 13-\frac{1}{2}a.

$$b=-\frac{\frac{5xy}{4}}{-\frac{a}{2}+13}$$

Divide -\frac{5xy}{4} by 13-\frac{1}{2}a.

$$b=-\frac{5xy}{2\left(26-a\right)}$$