Question

Solve the following pair of equations by reducing them to a pair of linear equations:$6x+3y=6xy,2x+4y=5xy$

• A. $x=1,y=1$
• B. $x=1,y=2$
• C. $x=0,y=1$
• D. None of these

Answer 1

Answer: (B)

$x=1,y=2$

$6x+3y=6xy$ .........Given

Multiply by $\frac{1}{xy}$ we get

$\frac{6x}{xy}+\frac{3y}{xy}=\frac{6xy}{xy}$

$\frac{6}{y}+\frac{3}{x}=\mathrm{6............}eq1$

$2x+4y=5xy$ ...........Given

Multiply with $\frac{1}{xy}$we get

$\frac{2x}{xy}+\frac{4y}{xy}=\frac{5xy}{xy}$

$\frac{2}{y}+\frac{4}{x}=\mathrm{5........}eq2$

Let $\frac{1}{x}=aand\frac{1}{y}=b$

$a+2b=\mathrm{2.......}eq3$
$4a+2b=\mathrm{5.....}eq4$

Subtracting eq3 and eq4 we get
$-3a=-3$
$a=1$

Substituting a=1 in eq3 we get
$1+2b=2$
$2b=1$
$b=\frac{1}{2}$

Thus if $a=\frac{1}{x}=1\Rightarrow x=1$

If $b=\frac{1}{y}=\frac{1}{2}\Rightarrow y=2$

Hence $x=1$ and $y=2$