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Question
Find x and y if `[(x + y, y),(2x, x - y)] [(2),(-1)] = [(3),(2)]`
Solution
Given
`[(x + y, y),(2x, x - y)] [(2),(-1)] = [(3),(2)]`
⇒ `[(2x + 2y, -y),(4x, -x + y)] = [(3),(2)]`
⇒ `[(2x, + y),(3x, + y)] = [(3),(2)]`
Comparing the corresponding elements
2x + y = 3 ...(i)
3x + y = 2 ...(ii)
Subtracting, we get
–x = 1
⇒ x = –1
Substituting the value of x in (i)
2(–1) + y = 3
⇒ –2 + y = 3
⇒ y = 3 + 2 = 5
Hence x = –1, y = 5.
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