Option 3 : \(\frac{15}{4}\)
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10 Questions 50 Marks 7 Mins
Concept:
Let a pair of linear equation in two variable a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0
The condition of parallel lines or inconsistent equations.
\(\frac{{{a_1}}}{{{a_2}}} = \frac{{{b_1}}}{{{b_2}}} \ne \frac{c_1}{c_2}\)
Calculation:
Given equation of lines
3x + 2ky = 2 and 2x + 5y + 1 = 0
a1 = 3; a2 = 2
b1 = 2k; b2 = 5
c1 = -2; c2 = 1
Here, given lines are parallel
So that,
\(\frac{{{a_1}}}{{{a_2}}} = \frac{{{b_1}}}{{{b_2}}} \ne \frac{c_1}{c_2}\)
\(\therefore \frac{3}{2} = \frac{2k}{{5}}\left( {\because{c_1} \ne {c_2}} \right)\)
∴ \(k=\frac{15}{4}\)
Additional Information
(I) If \(\frac{{{a_1}}}{{{a_1}}} \ne \frac{{{b_1}}}{{{b_2}}}\)
Then the graph will be a pair of lines interesting at a unique point. Which is the solution of the pair of equations.
(II) If
\(\frac{{{a_1}}}{{{a_2}}} = \frac{{{b_1}}}{{{b_2}}} = \frac{c_1}{{{c_2}}}\) then
Then graph will be a pair of coincident lines
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