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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