Question

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Answer 1

Question:

If x = 1, y = - 3 is the solution of the equations ax + by = 3ab and $\displaystyle{\sf\:\dfrac{x}{a}\:+\:\dfrac{y}{b}\:=\:2}$, find a and b.

Answer:

The values of a and b are

$\displaystyle{{\boxed{\red{\sf\:a\:=\:-\:\dfrac{8}{11}}}}\:\sf\:\&\:{\boxed{\red{\sf\:b\:=\:-\:\dfrac{8}{9}}}}}$

Option c)

Step-by-step-explanation:

The given equations are

ax + by = 3ab &

$\displaystyle{\sf\:\dfrac{x}{a}\:+\:\dfrac{y}{b}\:=\:2}$

We have given that x = 1 and y = - 3.

By substituting these values in first equation, we get,

ax + by = 3ab

⇒ a * 1 + b * - 3 = 3ab

⇒ a - 3b = 3ab

⇒ a = 3ab + 3b $\displaystyle{\sf\:\qquad\dots\:(\:1\:)}$

Now, by substituting the values in second equation,

$\displaystyle{\sf\:\dfrac{x}{a}\:+\:\dfrac{y}{b}\:=\:2}$

$\displaystyle{\implies\sf\:\dfrac{1}{a}\:+\:\dfrac{-\:3}{b}\:=\:2}$

$\displaystyle{\implies\sf\:\dfrac{1}{a}\:-\:\dfrac{3}{b}\:=\:2}$

$\displaystyle{\implies\sf\:\dfrac{b\:-\:3a}{ab}\:=\:2}$

$\displaystyle{\implies\sf\:b\:-\:3a\:=\:2\:ab}$

$\displaystyle{\implies\sf\:b\:-\:3\:(\:3\:ab\:+\:3b\:)\:=\:2\:ab\:\qquad\:\dots\:[\:From\:(\:1\:)\:]}$

$\displaystyle{\implies\sf\:b\:-\:9\:ab\:-\:9b\:=\:2\:ab}$

$\displaystyle{\implies\sf\:b\:-\:9b\:=\:2\:ab\:+\:9\:ab}$

$\displaystyle{\implies\sf\:-\:8b\:=\:11\:ab}$

$\displaystyle{\implies\sf\:-\:\dfrac{8}{11}\:=\:\dfrac{a\:\cancel{b}}{\cancel{b}}}$

$\displaystyle{\implies\boxed{\pink{\sf\:a\:=\:-\:\dfrac{8}{11}}}}$

Now, by substituting this value in equation ( 1 ),

$\displaystyle{\sf\:a\:=\:3ab\:+\:3b}$

$\displaystyle{\implies\sf\:-\:\dfrac{8}{11}\:=\:3\:\times\:\dfrac{-\:8}{11}\:b\:+\:3b}$

$\displaystyle{\implies\sf\:-\:\dfrac{24}{11}\:b\:+\:3b\:=\:-\:\dfrac{8}{11}}$

$\displaystyle{\implies\sf\:\dfrac{-\:24\:b\:+\:33\:b}{\cancel{11}}\:=\:-\:\dfrac{8}{\cancel{11}}}$

$\displaystyle{\implies\sf\:9b\:=\:-\:8}$

$\displaystyle{\implies\boxed{\pink{\sf\:b\:=\:-\:\dfrac{8}{9}}}}$

∴ The values of a and b are

$\displaystyle{\underline{\boxed{\red{\sf\:a\:=\:-\:\dfrac{8}{11}}}}\:\sf\:\&\:\underline{\boxed{\red{\sf\:b\:=\:-\:\dfrac{8}{9}}}}}$

Answer 2

Answer:

see the image hope that will be helpful to you to do your work if not then your answer is

$option \: b \: is \: the \: correct \: answer \: \\ \\ b)b = - \frac{8}{9}$