Question

9) The solution of the equation a x+by+ 5 = 0 and x - a y- 12 = 0 is
(2, -3)
Find the values of a and b.

Answer 1

Given Equations -

• ax + by + 5 = 0
• x - ay - 12 = 0

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To find -

• Value of a and b.

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Solution -

It is given that, solution of the given equations is (2, -3). Therefore, point (2, -3) satisfy the both equations.

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For first equation

$\tt\dashrightarrow{a(2) + b(-3) + 5 = 0}$

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$\tt\dashrightarrow{2a - 3b + 5 = 0}$

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$\tt\dashrightarrow{2a - 3b = -5}$ ⠀⠀...[1]

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For second equation

$\tt\dashrightarrow{2 - a(-3) - 12 = 0}$

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$\tt\dashrightarrow{2 + 3a = 12}$

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$\tt\dashrightarrow{3a = 12 - 2}$

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$\tt\dashrightarrow{3a = 10}$

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$\bf\dashrightarrow{a = \dfrac{10}{3}}$

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Putting the value of a in eq[1]

$\tt\dashrightarrow{2 \times \dfrac{10}{3} - 3b = -5}$

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$\tt\dashrightarrow{\dfrac{20}{3} - 3b = -5}$

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$\tt\dashrightarrow{\dfrac{20 - 9b}{3b} = -5}$

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$\tt\dashrightarrow{20 - 9b = -15b}$

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$\tt\dashrightarrow{-9b + 15b = -20}$

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$\tt\dashrightarrow{6b = -20}$

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$\tt\dashrightarrow{b = \dfrac{-20}{6}}$

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$\bf\dashrightarrow{b = \dfrac{-10}{3}}$

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Hence,

• Value of $\sf{a = \dfrac{10}{3}}$ and $\sf{b = \dfrac{-10}{3}}$

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