If $2 a = b$ , the pair of equations $a x + b y = 2 a^{2} - 3 b^{2}, x + 2 y = 2 a - 6 b$ possess

no solutions

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only one solutions

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only two solutions

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an infinite number of solutions

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Solution

The correct option is C an infinite number of solutions
Given, $a x + b y = 2 a^{2} 3 b^{2}$
Substituting $b = 2 a$ in it, and simplifying we get
$x + 2 y = - 10 a$ --- (1)
Also, given $x + 2 y = 2 a - 6 b$
Substituting $b = 2 a$ in it, and simplifying we get
$x + 2 y = - 10 a$ -- (2)
Since the equations $1$ and $2$ are exactly same, the equations have infinitely many solutions.

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Similar questions

2 a = b

x + 2 y = 2 a - 6 b, a x + b y = 2 a^{2} - 3 b^{2}

2 a = b

a x + b y = 2 a^{2} - 3 b^{2}, x + 2 y = 2 a - 6 b

For what value of a and b will the following pair of equations have infinite solution.

x+2y = 1

(a-b)x + (a+b)y =2a-b+1

2 a + 6 b - 3 (a + 3 b)^{2}

2 a + 6 b - 3 (a + 3 b)^{2}

= 2 (a + 3 b) - 3 (a + 3 b)^{2} [T a k i n g 2 c o m m o n f r o m 2 a + 6 b]

= (a + 3 b) {\begin{matrix} 2 - 3 (a + 3 b) \end{matrix}} [T a k i n g (a + 3 b) c o m m o n]

= (a + 3 b) (2 - 3 a - 9 b)

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