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Question
If `[(5, 2),(-1, y + 1)] -2 [(1, 2x - 1),(3, -2)] = [(3, -8),(-7, 2)]` Find the values of x and y
Solution
`[(5, 2),(-1, y + 1)] -2 [(1, 2x - 1),(3, -2)] = [(3, -8),(-7, 2)]`
⇒ `[(5, 2),(-1, y + 1)] - [(2, 4x - 2),(6, -4)] = [(3, -8),(-7, 2)]`
⇒ `[(5 - 2, 2 - 4x + 2),(-1 - 6, y + 1 + 4)] = [(3, -8),(-7, 2)]`
⇒ `[(3, 4 - 4x),(-7, y + 5)] = [(3, -8),(-7, 2)]`
Comparing the corresponding terms, we get
4 – 4x = –8
⇒ –4x = –8 – 4
⇒ –4x = –12
⇒ x = `(-12)/(-4)` = 3
and
y + 5 = 2
⇒ y = 2 – 5 = –3
∴ x = 3, y = –3.
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