Question

Find the solution set of the system of equations: $\frac{4}{x}+5y=7and\frac{3}{x}+4y=5.$

• A. $(\frac{1}{3},-1)$
• B. $(\frac{1}{3},-3)$
• C. $(\frac{1}{3},-2)$
• D. $(\frac{1}{3},1)$

Answer 1

Answer: (A)

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

We put $\frac{1}{x}=p$

Then the system of given equations becomes

$4p+5y=\mathrm{7............}\left(i\right)$ &

$3p+4y=\mathrm{5........}\left(ii\right)$

$\left(i\right)\times 3\Rightarrow 12p+15y=\mathrm{21........}\left(iii\right)\&\left(ii\right)\times 4\Rightarrow 12p+16y=\mathrm{20.........}\left(iv\right).\left(iii\right)-\left(iv\right)\Rightarrow -y=1\Rightarrow y=-1.$

Putting $y=-1$ in $\left(i\right)$,

$4p+5\times (-1)=7\Rightarrow p=\frac{12}{4}=3.\therefore x=\frac{1}{3}.\therefore (x,y)=(\frac{1}{3},-1).$

Hence, the answer is $(\frac{1}{3},-1)$