Given 3x - 4y = 7 and x + cy = 13 for what value of "c" will the two equation not have a solution ?

\frac{3}{4}

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\frac{4}{3}

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-4

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\frac{- 4}{3}

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Solution

The correct option is B $\frac{- 4}{3}$
Given
$3 x - 4 y = 7$ .........eq(1)
$x + c y = 13$ ..........eq(2)
We know that,
If the system of equations have no solution then,
$\frac{a 1}{a 2} = \frac{b 1}{b 2} \neq \frac{c 1}{c 2}$
so,
$\frac{a 1}{a 2} = \frac{b 1}{b 2}$
$\Rightarrow \frac{3 x}{x} = \frac{- 4 y}{c y}$
$\Rightarrow 3 c = - 4$
$c = - \frac{4}{3}$

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Check whether the value given in the brackets is a solution to the given equation or not:

(a) n + 5 = 19 (n = 1) (b) 7n + 5 = 19 (n = − 2)

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