Question

2/x+3/y=5;3/x-1/y+9=0 solve by cross multiplication

Answer 1

Answer:  The answer is $x=-\dfrac{1}{2},~~y=\dfrac{1}{3}.$.

Step-by-step explanation:  Since we are to solve the given pair of equations by cross-multiplication, so let us take

$\dfrac{1}{x}=a,~~~\dfrac{1}{y}=b.$

Then the given equations become

$2a+3b=5,\\\\3a-b=-9.$

Multiplying the second equation by 3 and the adding to the first equation, we have

$2a+9a=5-27\\\\\Rightarrow 11a=-22\\\\\Rightarrow a=-2.$

Therefore,

$3\times (-2)-b=-9\\\\\Rightarrow -6-b=-9\\\\\Rightarrow b=-6+9\\\\\Rightarrow b=3.$

Hence,

$x=\dfrac{1}{a}=\dfrac{1}{-2}=-\dfrac{1}{2},$

and

$y=\dfrac{1}{b}=\dfrac{1}{3}.$

Thus the solution is

$x=-\dfrac{1}{2},~~y=\dfrac{1}{3}.$