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Solve for X and Y: [(2, 5),(5, 2)][(X),(Y)] = [(-7),(14)] - ICSE Class 10 - Mathematics

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Question

Solve for x and y: `[(2, 5),(5, 2)][(x),(y)] = [(-7),(14)]`

Solution

`[(2, 5),(5, 2)][(x),(y)] = [(-7),(14)]`

`[(2x + 5y),(5x + 2y)] = [(-7),(14)]`

Comparing the corresponding elements, we get

2x + 5y = -7 ....(1)

5x + 2y = 14 ....(2)

Myultiplying (1) and 2 and  (2) with 5 we get

4x + 10y = -14...(3)

25x + 10y = 70 ....(4)

Substracting (3) from (4), we get

21x = 84 => x = 4

From (2), 2y = 14 - 5x = 14 - 20 = -6 => y = -3

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Solution Solve for X and Y: [(2, 5),(5, 2)][(X),(Y)] = [(-7),(14)] Concept: Multiplication of Matrix.
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