Solution: Given, the pair of equations is 3x - y + 8 = 0 6x - ky = -16 represent coincident lines. 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 \(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}\), then the pair of linear equations is dependent and consistent. Here, a₁ = 3, b₁ = -1, c₁ = 8 a₂ = 6, b₂ = -k, c₂ = 16 So, a₁/a₂ = 3/6 = 1/2 b₁/b₂ = -1/-k = 1/k c₁/c₂ = 8/16 = 1/2 \(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}=\frac{1}{2}\) \(\frac{1}{k}=\frac{1}{2}\) Therefore, the value of k is 2. ✦ Try This: For what value of k, do the equations x - y + 8 = 0 and 3x - ky = -24 represent coincident lines? Given, the pair of equations are x - y + 8 = 0 3x - ky = -24 represent coincident lines. We have to find the value of k. Here, a₁ = 1, b₁ = -1, c₁ = 8 a₂ = 3, b₂ = -k, c₂ = 24 So, a₁/a₂ = 1/3 b₁/b₂ = -1/-k = 1/k c₁/c₂ = 8/24 = 1/3 \(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}=\frac{1}{3}\) \(\frac{1}{k}=\frac{1}{3}\) Therefore, the value of k is 3 ☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3 NCERT Exemplar Class 10 Maths Exercise 3.1 Problem 6 Summary: For the value of k = 2, the equations 3x - y + 8 = 0 and 6x - ky = -16 represent coincident lines. ☛ Related Questions: |