Which of the following pairs of equations represents coincident lines?
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2x + y = 4, 3x + y = 5
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x + 2y = 7, 2x + 4y = 14
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x – y = 5, 2x + 3y = 25
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2x – 7y = 7, x + y = 8
Reveal answer
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B
Correct answer
Explanation
For the pair of equations to represent coincident lines, $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$ In lines x + 2y = 7 and 2x + 4y = 14, $\frac{a_1}{a_2} = \frac{1}{2}, \frac{b_1}{b_2} =\frac{2}{4} =\frac{1}{2}, \frac{c_1}{c_2} = \frac{7}{14} = \frac{1}{2}$ So, $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$
AI explanation
Coincident lines occur when the ratios of corresponding coefficients are all equal: a1/a2 = b1/b2 = c1/c2. For x+2y=7 and 2x+4y=14, the ratios are 1/2 = 2/4 = 7/14, all equal to 0.5, so the two equations represent the same line.