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प्रश्न
Solve the following equations by the reduction method.
5x + 2y = 4, 7x + 3y = 5
उत्तर
`[(5,2),(7,3)][("x"),("y")]=[(4),(5)]`
This is the form AX = B,
Where A = `[(5,2),(7,3)][("x"),("y")] and "B" =[(4),(5)]`
Applying `"R"_2 →"R"_2 - "R"_1`, we get
`[(5,2),(2,1)][("x"),("y")]=[(4),(1)]`
Applying `"R"_1 →"R"_1 - 2"R"_2`, we get
`[(1,0),(2,1)][("x"),("y")]=[(2),(1)]`
∴ `[(x + 0),(2x + y)]=[(2),(1)]`
∴ By equality of matrics, we get
x = 2 ...(i)
2x + y = 1 ...(ii)
Substituting x = 2 in equation (ii), we get
2(2) + y = 1
∴ y = 1 - 4 = - 3
∴ x = 2 and y = - 3 is the required solution.
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