Question

Solve for x and y using cross multiplication method :

$\frac{5}{(x+y)}-\frac{2}{(x-y)}+1=0\frac{15}{(x+y)}+\frac{7}{(x-y)}-10=0(x\ne y,x\ne -y)$

• A.
  3 and 2
• B.
  4 and 1
• C.
  5 and 0
• D.
  2 and 3

Answer 1

The correct option is A

3 and 2
$\frac{5}{(x+y)}-\frac{2}{(x-y)}+1=\mathrm{0...}\left(1\right)\frac{15}{(x+y)}+\frac{7}{(x-y)}-10=\mathrm{0...}\left(2\right)Let\frac{1}{x+y}=a,\frac{1}{x-y}=b5a-2b+1=\mathrm{0...}\left(3\right)15a+7b-10=\mathrm{0....}\left(4\right)$

By Cross-multiplication mehod

$\frac{a}{20-7}=\frac{b}{15-(-50)}=\frac{1}{35-(-30)}\frac{a}{13}=\frac{b}{65}=\frac{1}{65}\Rightarrow \frac{a}{13}=\frac{1}{65}\Rightarrow a=\frac{13}{65}\Rightarrow a=\frac{1}{5}\Rightarrow \frac{6}{65}=\frac{1}{65}\Rightarrow b=\frac{65}{65}\Rightarrow b=1\because a=\frac{1}{5},b=1\Rightarrow \frac{1}{x+y}=\frac{1}{5}\Rightarrow \frac{1}{x-y}=1\therefore x+y=5\therefore x-y=1$

By cross- multiplication method :

$\frac{x}{1-(-5)}=\frac{y}{5-1}=\frac{-1}{-1-1}\frac{x}{6}=\frac{y}{4}=\frac{-1}{-2}\Rightarrow \frac{x}{6}=\frac{1}{2}\Rightarrow x=3\Rightarrow \frac{y}{4}=\frac{-1}{-2}\Rightarrow y=2$


Hence, option a is correct.