Saved Bookmarks
| 1. |
Find the values of p and q for which the following system of linear equations has infinite number of solutions : 2x + 3y = 1, (p + q)x + (2p – q)y = 21 |
|
Answer» The given equations are : 2x + 3y –1 = 0 and (p + q)x + (2p – q)y – 21 = 0 Here, a1 = 2, b1 = 3, c1 = –1 and a2 = p + q, b2 = 2p – q, c2 = – 21 For infinite solutions, \(\frac{a_1}{a_2}\) = \(\frac{b_1}{b_2}\)= \(\frac{c_1}{c_2}\) \(\Rightarrow\) \(\frac{2}{p+q}\) = \(\frac{3}{2p-q}\) = \(\frac{-1}{-21}\) \(\Rightarrow\) \(\frac{2}{p+q}\) = \(\frac{1}{21}\) and \(\frac{3}{2p-q}\) = \(\frac{1}{21}\) \(\Rightarrow\) p + q = 42 Adding (1) and (2), we get 3p = 105 \(\Rightarrow\) p = 35 Putting p = 35 in (1), we get 35 + q = 42 \(\Rightarrow\) q = 42 - 35 = 7 \(\therefore\) p = 35, q = 7 |
|