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Question
If \[x\binom{2}{3} + y\binom{ - 1}{1} = \binom{10}{5}\] , find the value of x.
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Solution
` x[[ 2],[3]] +y [[- 1],[1]] = [[10],[5]]`
`[[2x - y ] , [3x + y] ]`=` [[10 ] , [ 5]]`
Corresponding elements of equal matrices are equal .
\[ \Rightarrow 2x - y = \text{10 and } 3x + y = 5\]
\[ \Rightarrow y =\text{2x - 10 and }3x + \left( 2x - 10 \right) = 5\]
\[ \Rightarrow y = \text{2x - 10 and }5x = 15\]
\[ \Rightarrow y = \text{2x - 10 and }x = 3\]
\[ \Rightarrow y = 2\left( 3 \right) - \text{10 and }x = 3\]
\[ \Rightarrow y = \text{- 4 and}x = 3\]
Hence, the value of x is 3.
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