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प्रश्न
Solve the following equations by the reduction method.
3x – y = 1, 4x + y = 6
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उत्तर
The given equations can be written in the matrix form as:
`[(3,-1),(4,1)][("x"),("y")]=[(1),(6)]`
By 4R1 and 3R2, we get,
`[(12,-4),(12,3)][("x"),("y")]=[(4),(18)]`
By R2 – R1, we get,
`[(12,-4),(0,7)][("x"),("y")]=[(4),(14)]`
∴ `[(12"x"-4"y"),(0+7"y")]=[(4),(14)]`
By equality of matrices,
12x − 4y = 4 ........(1)
7y = 14 .............(2)
From (2), y = 2
Substituting y = 2 in (1), we get,
12x − 8 = 4
∴ 12x = 12
∴ x = 1
Hence, x = 1, y = 2 is the required solution.
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