Question

Solve the following system of equations by elimination method.

$11x-7y=xy,9x-4y=6xy$

• A. $(\frac{1}{3},\frac{1}{2})$
• B. $(\frac{1}{2},\frac{1}{2})$
• C. $(\frac{1}{3},\frac{1}{3})$
• D. None of these

Answer 1

Answer: (A)

$(\frac{1}{3},\frac{1}{2})$

$11x-7y=xy;9x-4y=6xy$

$\frac{11}{y}-\frac{7}{x}=1$ .....eq1

$\frac{9}{y}-\frac{4}{x}=6\Rightarrow \frac{1}{4}(\frac{9}{y}-6)=\frac{1}{x}$ , put this value in eq1

$\Rightarrow$ $\frac{11}{y}-7\left[\frac{1}{4}(\frac{9}{y}-6)\right]=1$

$y=\frac{1}{2}$

Put $y=\frac{1}{2}$ in eq1, we get

$11x-7\times \frac{1}{2}=\frac{x}{2}$

$x=\frac{1}{3}$