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Question
Solve the following for x and y: \[\begin{bmatrix}3 & - 4 \\ 9 & 2\end{bmatrix}\binom{x}{y} = \binom{10}{ 2}\]
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Solution
Here,
\[\begin{bmatrix}3 & - 4 \\ 9 & 2\end{bmatrix}\binom{x}{y} = \binom{10}{2}\]
\[ \Rightarrow \binom{3x - 4y}{9x - 2y} = \binom{10}{2}\]
\[ \Rightarrow 3x - 4y = 10 . . . (1) \]
\[ 9x + 2y = 2 . . . (2)\]
Solving both the equations, we get
\[x = \frac{14}{21}\]
\[ = \frac{2}{3}\]
Substituting the value of x in eq. (1), we get
\[3 \times \frac{2}{3} - 4y = 10\]
\[ \Rightarrow 2 - 4y = 10\]
\[ \Rightarrow 4y = - 8\]
\[ \Rightarrow y = - 2\]
\[ \therefore x = \frac{2}{3}\text{ and }y = - 2\]
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