InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Solve the equation by reduction method :x + 3y = 2, 3x + 5y = 4. |
|
Answer» Given, x + 3y = 2, 3x + 5y = 4. The given equations can be written in the matrix form as : \( \begin{bmatrix} 1 & 3 \\[0.3em]3 &5 \\[0.3em] \end{bmatrix} \) \( \begin{bmatrix} x \\[0.3em] y\\[0.3em] \end{bmatrix} \) = \( \begin{bmatrix} 2 \\[0.3em] 4\\[0.3em] \end{bmatrix} \) By R2 – 3R1, we get \( \begin{bmatrix} 1 & 3 \\[0.3em]0 &-4 \\[0.3em] \end{bmatrix} \)\( \begin{bmatrix} x \\[0.3em] y\\[0.3em] \end{bmatrix} \) = \( \begin{pmatrix} 2 \\[0.3em] -2\\[0.3em] \end{pmatrix} \). ∴ \( \begin{bmatrix} x+3 \\[0.3em] 0-4y\\[0.3em] \end{bmatrix} \) = \( \begin{bmatrix} 2 \\[0.3em] -2\\[0.3em] \end{bmatrix} \) By equality of matrices, x + 3y = 2 …(1) - 4y = - 2 From (1), y = \(\frac{1}{2}\) Substituting y = \(\frac{1}{2}\) in (1), we get, x + \(\frac{3}{2}\) = 2 ∴ x = 2 – \(\frac{3}{2}\) = \(\frac{1}{2}\) Hence, x = \(\frac{1}{2}\), y = \(\frac{1}{2}\) is the required solution. |
|