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प्रश्न
Solve the following systems of equations:
x + y = 5xy
3x + 2y = 13xy
उत्तर
The given system of equation is
x + y = 5xy ....(i)
3x + 2y = 13xy ....(ii)
Multiplying equation (i) by 2 and equation (ii) by , we get
2x + 2y = 10xy ....(iii)
3x + 2y = 13xy ....(iv)
Subtracting equation (iii) from equation (iv), we get
3x - 2x = 13xy - 10xy
=> x = 3xy
`=> x/(3y) = y`
`=> y = 1/3`
Putting y = 1/3 in equation (i), we get
`x + y = 5 xx x xx 1/3`
`x + 1/3 = (5x)/3`
`=> 1/3 = (5x)/3 - x`
`=> 1/3 = (5x - 3x)/3`
=> 1 = 2x
=> 2x = 1
`=> x = 1/2`
Hence, solution of the given system of equations is `x = 1/2, y = 1/3`
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