The pair of equations 4 x -3 y -12-0 and 2 x -3 y -15-0 hasA- a unique solutionB- infinitely many solutionsC- no solutionD- 2 solutions

The correct option is A a unique solution Given equations 4x 3y +12 = 0 and 2x +3y 15 = 0 a_1/a_2 = 4/2 = 2 and b_1/b_2 = 3/3 = 1 ⇒a_1/a_2 ≠ b_1/b_2 The ...

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Standard IX

Mathematics

Role of Coefficients and Constants

The pair of e...

Question

The pair of equations $4 x - 3 y + 12 = 0$ and $2 x + 3 y - 15 = 0$ has

a unique solution

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infinitely many solutions

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no solution

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2 solutions

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Solution

The correct option is A
a unique solution

Given equations

$4 x - 3 y + 12 = 0$ and $2 x + 3 y - 15 = 0$

$\frac{a_{1}}{a_{2}} = \frac{4}{2} = 2$ and $\frac{b_{1}}{b_{2}} = \frac{- 3}{3} = - 1$

$\Rightarrow \frac{a_{1}}{a_{2}}$ ≠ $\frac{b_{1}}{b_{2}}$

Therefore, the given pair of equations has a unique solution.

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The pair of equations 4x−3y+12=0 and 2x+3y−15=0 has

The correct option is A a unique solution Given equations 4x−3y+12=0 and 2x+3y−15=0 a1a2=42=2 and b1b2=−33=−1 ⇒a1a2 ≠ b1b2 Therefore, the given pair of equations has a unique solution.

The pair of equations $4 x - 3 y + 12 = 0$ and $2 x + 3 y - 15 = 0$ has