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Question

$$\dfrac{1}{3}x - \dfrac{1}{6}y = 4$$
$$6x - ay = 8$$
In the system of equations above, $$a$$ is a constant. If the system has no solution, what is the value of $$a$$


A
13
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B
1
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C
3
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D
0
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Solution

The correct option is C $$3$$
$$\dfrac{1}{3}x - \dfrac{1}{6}y = 4$$
$$6x - ay = 8$$
condition for no solution 
$$\dfrac{{{a_1}}}{{{a_2}}} = \dfrac{{{b_1}}}{{{b_2}}} \ne \dfrac{{{c_1}}}{{{c_2}}}$$
$$\dfrac{\dfrac 13}{6} = \dfrac{{\dfrac{{ - 1}}{6}}}{{ - a}} \ne \dfrac{4}{8}$$
$$6a = 6 \times 3$$
$$a = 3$$

Mathematics

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