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Question
Solve the following systems of equations:
23x − 29y = 98
29x − 23y = 110
Solution
The given system of equation is
23x − 29y = 98 ....(i)
29x − 23y = 110 ...(ii)
Adding equation (i) and equation (ii), we get
23x + 29x - 29y - 23y = 98 + 110
=> 52x - 52y = 208
=> 52 (x - y) = 208
`=> x - y = 208/52 = 4`
=> x - y - 4 ...(iii)
Subtracting equation (i) by equation (ii), we get
29x - 23x - 23y + 29y = 110 - 98
=> 6x + 6y = 12
=> 6(x + y) = 12
`=> x + y = 12/6 = 2`
=> x = y = 2 ...(iv)
Adding equation (iii) and equation (iv), we get
2x = 2 + 4 = 6
Putting x = 3 in equation (iv), we get
3 + y = 2
=>? y = 2- 3 = -1
Hence, solution of the given system of equation is x = 3 , y = -1
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