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Question
Solve for x and y: `x[(2),(1)] + y[(3),(5)] + [(-8),(-11)]` = O
Solution
Given that: x = `x[(2),(1)] + y[(3),(5)] + [(-8),(-11)]` = O
L.H.S. `x[(2),(1)] + y[(3),(5)] + [(-8),(-11)]` = O
⇒ `[(2x),(x)] + [(3y),(5y)] + [(-8),(-11)]` = O
⇒ `[(2x + 3y - 8),(x + 5y - 11)] =[(0),(0)]`
Comparing the corresponding elements of both sides, we get,
2x + 3y – 8 = 0
⇒ 2x + 3y = 8 .....(1)
x + 5y – 11 = 0
⇒ x + 5y = 11 ......(2)
Multiplying equation (1) by 1 and equation (2) by 2, and then on subtracting, we get,
2x + 3y = 8
2x + 10y = 22
(–) (–) (–)
–7y = –14
∴ y = 2
Putting y = 2 in equation (2) we get,
x + 5 × 2 = 11
⇒ x + 10 = 11
x = 11 – 10 = 1
Hence, the values of x and y are 1 and 2 respectively.
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