Question

solve 3/x-2/y=0 and 2/x+5/y=19.hence find p if y=px+3

Answer 1

Answer:

The value of p is -16/3

Step-by-step explanation:

$\frac{3}{x}-\frac{2}{y}=0$

$\frac{2}{x}+\frac{5}{y}=19$

Take $\frac{1}{x}=a\:and\:\frac{1}{y}=b$ we get

$3a-2b=0$.........(1)

$2a+5b=19$......(2)

(1)*2$\implies\:6a-4b=0$

(2)*3$\implies\:6a+15b=57$

subtracting, we get

-19b=-57

b=3

put b=3 in (2)

2a+15=19

2a=4

a=2

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

$\implies\:x=\frac{1}{a}$

$\implies\:x=\frac{1}{2}$

$\implies\:y=\frac{1}{3}$

Now,

$y=px+3$

$\implies\:\frac{1}{3}=p(\frac{1}{2})+3$

$\implies\:\frac{1}{3}-3=\frac{p}{2}$

$\implies\:\frac{1-9}{3}=\frac{p}{2}$

$\implies\:\frac{-8}{3}=\frac{p}{2}$

$\implies\:p=\frac{-16}{3}$

Answer 2

Answer:

−y2=0

\frac{2}{x}+\frac{5}{y}=19x2+y5=19

Take \frac{1}{x}=a\:and\:\frac{1}{y}=bx1=aandy1=b we get

3a-2b=03a−2b=0 .........(1)

2a+5b=192a+5b=19 ......(2)

(1)*2\implies\:6a-4b=0⟹6a−4b=0

(2)*3\implies\:6a+15b=57⟹6a+15b=57

subtracting, we get

-19b=-57

b=3

put b=3 in (2)

2a+15=19

2a=4

a=2

\frac{1}{x}=ax1=a

\implies\:x=\frac{1}{a}⟹x=a1

\implies\:x=\frac{1}{2}⟹x=21

\implies\:y=\frac{1}{3}⟹y=31

Now,

y=px+3y=px+3

\implies\:\frac{1}{3}=p(\frac{1}{2})+3⟹31=p(21)+3

\implies\:\frac{1}{3}-3=\frac{p}{2}⟹31−3=2p

\implies\:\frac{1-9}{3}=\frac{p}{2}⟹31−9=2p

\implies\:\frac{-8}{3}=\frac{p}{2}⟹3−8=2p

\implies\:p=\frac{-16}{3}⟹p=3−16