InterviewSolution
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InterviewSolution
| 1. |
Px +qy = p-q Qx-py =p+q |
| Answer» The given pair of equations ispx + qy = p - q .....(1)qx - py = p + q ....(2)Multiplying equation (1) by p and equation (2) by q, we getp2x + pqy = p2 - pq....(3)q2x - pqy = pq + q2.....(4)Adding equation (3) and equation (4), we get(p2 + q2)x = p2 + q2{tex}\\Rightarrow \\;x = \\frac{{{p^2} + {q^2}}}{{{p^2} + {q^2}}} = 1{/tex}Substituting this value of x in equation (1), we getp(1) + qy = p - q{tex}\\Rightarrow{/tex} qy = -q{tex}\\Rightarrow \\;y = \\frac{{ - q}}{q} = - 1{/tex}So, the solution of the given pair of linear equations is x = +1, y = -1.Verification, Substituting x = 1, y = -1,We find that both the equations (1) and (2) are satisfied as shown below:px + qy = p(1) + q(-1) = p - qqx - py = q(1) - p(-1) = q + p = p + qThis verifies the solution. | |