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Question

Given that $$kx - 3y = 4$$and $$4x - 5y = 7$$
In the system of equations above, $$k$$ is a constant and $$x$$ and $$y$$ are variables. For what value of $$k$$ will the system of equations have no solution?


A
125
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B
167
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C
167
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D
125
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Solution

The correct option is A $$\dfrac {12}{5}$$
Let $$kx - 3y = 4 $$ ..(1)
and $$4x - 5y = 7 $$ ..(2)
Multiplying equation (1) by $$5$$ and equation (2) by $$3$$, we have
$$5kx - 15y = 20 $$ ..(3)
$$12x - 15y = 21 $$ ..(4)
Since the coefficient of $$y$$ is same in equations (3) and (4), and the terms on right hand side of equality are different, the coefficients of $$x$$ cannot be the same.
$$\therefore 5k \neq 12$$
$$\therefore k \neq \cfrac{12}{5}$$

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