Solution: Show Given, the linear pair of equations are 3x + 2ky = 2 2x + 5y + 1 = 0 We have to find the value of k. We know that, For a pair of linear equations in two variables be a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, If \(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}\neq \frac{c_{1}}{c_{2}}\), then the graph will be a pair of parallel lines. Here, a₁ = 3, b₁ = 2k, c₁ = -2 a₂ = 2, b₂ = 5, c₂ = 1 So, a₁/a₂ = 3/2 b₁/b₂ = 2k/5 c₁/c₂ = -2/1 = -2 By using the above result, \(\frac{3}{2}=\frac{2k}{5}\) On cross multiplication, 3(5) = 2(2k) 15 = 4k So, k = 15/4 Therefore, the value of k is 15/4. ✦ Try This: If the lines given by 2x + 3ky = 2 and 3x + 5y + 1 = 0 are parallel, then the value of k is Given, the linear pair of equations are 2x + 3ky = 2 3x + 5y + 1 = 0 We are required to find the value of k. Here, a₁ = 2, b₁ = 3k, c₁ = -2 a₂ = 3, b₂ = 5, c₂ = 1 So, a₁/a₂ = 2/3 b₁/b₂ = 3k/5 c₁/c₂ = -2/1 = -2 By using the above result, \(\frac{2}{3}=\frac{3k}{5}\) On cross multiplication, 2(5) = 3(3k) 10 = 9k So, k = 10/9 Therefore, the value of k is 10/9 ☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3 NCERT Exemplar Class 10 Maths Exercise 3.1 Problem 7 Summary: If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the value of k is 15/4 ☛ Related Questions: The given system of equations may be written as x + 2y + 7 = 0 2x + ky + 14 = 0 The given system of equations is of the form `a_1x + b_1y + c_1 = 0` `a_2x + b_2y + c_2 = 0` Where `a_1 = 1, b_1 = 2, c_1 = 7` And `a_2 = 2,b_2 = k, c_2 = 14` The given equations will represent coincident lines if they have infinitely many solutions, The condition for which is `a_1/a_2 = b_1/b_2 = c_1/c_2 =. 1/2 = 2/k = 7/14 => k = 4` Hence, the given system of equations will represent coincident lines, if k = 4
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