Question

the solution of the system of linear equations 4/x+9/y=5 and 2/x+18/y=7 is​

Answer 1

✪AnSwEr

${\tt{\red{\underline{\large{Given}}}}}$

• solution of the system of linear equations
• 4/x+9/y=5 and
• 2/x+18/y=7

${\sf{\green{\underline{\large{To\:find}}}}}$

• value of x and y

${\sf{\pink{\underline{\Large{Explanation}}}}}$

4/x+9/y=5. and 2/x+18/y=7

let 1/x = a and 1/y =b

Then

4a+9b=5 ____(1)

2a+18b=7_____(2)

Multiplying by 2 in Equation 2

4a+36b=14______(3)

Solving equation (1) and (3)

4a+36b=14

4a+9b=5

______

27b=9

=>b=9/27 =1/3

=>4a+3=5

=>4a=2

=>a=1/2

Now

=>1/x=1/2

=>x=2

And

=>1/y = 1/3

=>y=3

4

Answer 2

AnsweR

$\bold{\frac{4}{x}+\frac{9}{y}=5 ...(1)}\\\\\bold{\frac{2}{x}+\frac{18}{y}=7 }\\\\\bold{Now\;multiply\;both\;sides\;of\;equations\;with\;2\;we,\;get\;,}\\\\\implies \bold{\frac{4}{x}+\frac{36}{y}=14 ...(2) }\\\\\bold{Now\;solving\;(2)-(1),\;we\;get\;,}$

$\implies \bold{(\frac{4}{x}+\frac{36}{y} )-(\frac{4}{x}+\frac{9}{y} )=14-5}\\\\\implies \bold{\frac{27}{y}=9 }\\\\\implies \bold{\bf{\red{y=3}}}$

$\bold{Now\;sub.\;y\;value\;in\;(1)\;,we\;get\;,}\\\\\implies \bold{\frac{4}{x}=5-\frac{9}{3} }\\\\\implies \bold{\frac{4}{x}=2}\\\\\implies \bold{\bf{\blue{x=2}}}$