• # question_answer If the graphs of the equations in the given situation are plotted on the same graph paper, then:      A) The lines will be parallel B) The lines will coincide C) The lines will intersect D) Can't say

Correct Answer: C

Solution :

 We can find whether lines will be intersecting, coincident or parallel, by calculating the ratios of the coefficients of the pair of linear equations. As the two equations are given by $x-y=4$ and      $3x-y=24$ Let us calculate the ratios of their coefficients $\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{1}{3};\,\,\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{-1}{-1}=1,\,\,\,\frac{{{c}_{1}}}{{{c}_{2}}}=\frac{4}{24}=\frac{1}{6}$ As, $\frac{{{a}_{1}}}{{{a}_{2}}}\ne \,\,\frac{{{b}_{1}}}{{{b}_{2}}},$ the two lines will intersect at a point. So, option [c] is correct.

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