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Question
Solve the following equations by the reduction method.
2x + y = 5, 3x + 5y = – 3
Solution
The given equations can be written in the matrix form as:
`[(2,1),(3,5)][("x"),("y")]=[(5),(-3)]`
By 2R2 , we get,
`[(2,1),(6,10)][("x"),("y")]=[(5),(-6)]`
By R2 – 3R1, we get,
`[(2,1),(0,7)][("x"),("y")]=[(5),(-21)]`
∴ `[(2"x"+"y"),(0+7"y")]=[(5),(-21)]`
By equality of matrices,
2x + y = 5 ........(1)
7y = − 21 ........(2)
From (2), y = − 3
Substituting y = − 3 in (1), we get,
2x − 3 = 5
∴ 2x = 8
∴ x = 4
Hence, x = 4, y = − 3 is the required solution.
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