Maharashtra BoardEnglish MediumSTD 12 ScienceMathsMatrics3 Marks
Question
Solve the following equations by reduction method $: 2x + y = 5, 3x + 5y = -3$
✓
Answer
The given equations can be written in the matrix form as $:\left[\begin{array}{ll}2 & 1 \\ 3 & 5\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{r}5 \\ -3\end{array}\right]$
By $2 \mathrm{R}_2$, we get,
$\left[\begin{array}{rr}2 & 1 \\ 6 & 10\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{r}5 \\ -6\end{array}\right]$
By $R_2-3 R_1$, we get,
$\left[\begin{array}{ll}2 & 1 \\ 0 & 7\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{r}5 \\ -21\end{array}\right]$
$\therefore\left[\begin{array}{l}2 x+y \\ 0+7 y\end{array}\right]=\left[\begin{array}{r}5 \\ -21\end{array}\right]$
By equality of matrices,
$2x + y = 5 …(1)$
$7y = -21 …(2)$
From $(2), y = -3$
Substituting $y = -3$ in $(1),$ we get,
$2x – 3 = 5$
$\therefore 2x = 8 $
$\therefore x = 4$
Hence, $x = 4, y = -3$ is the required solution.
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