Which of the following pairs of equations represents coincident lines?
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x + y = 2, 3x + 3y = 9
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x + 2y = 3, 4x + 8y = 12
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2x – y = 1, x – y = 0
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2x + 4y = 8, x + 2y = 16
Reveal answer
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B
Correct answer
Explanation
A pair of lines is coincident, if $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$. In lines, x + 2y = 3 and 4x + 8y = 12 $\frac{a_1}{a_2} = \frac{1}{4}, \frac{b_1}{b_2} =\frac{2}{8} = \frac{1}{4} , \frac{c_1}{c_2} = \frac{3}{12} = \frac{1}{4}$ $\therefore$ $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$
AI explanation
Coincident lines have all three coefficient ratios equal: a1/a2 = b1/b2 = c1/c2. For x+2y=3 and 4x+8y=12, the ratios are 1/4 = 2/8 = 3/12, all equal to 0.25, confirming the two equations describe the same line.