Question

5. Find whether the line represented by 2x+y=3 and 4x+2y=6are parallel,coincidentor
intersecting.​

Answer 1

$2x + y = 3 \\ 2x + y - 3 = 0 \:.............(1) \\ 4x + 2y = 6 \\ 4x + 2y - 6 = 0.............(2)$

eq (1) & (2) are in the form of quadratic equation

$now \\ a1 = 2 \\b1 = 1 \\ c1 = - 3 \\ a2 = 4 \\ b2 = 2 \\ c2 = - 6$

$\frac{a1}{a2} = \frac{2}{4} = \frac{1}{2}$

$\frac{b1}{b2} = \frac{1}{2}$

$\frac{c1}{c2} = \frac{ - 3}{ - 6} = \frac{1}{2}$

Therefore, the lines represented by the eq (1) and (2) are co-incident.

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