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Question

32x + 23y = 1313 ; 23x + 32y = 813


Solution

32x+23y=13139x+4y6=403 9x+4y= 80            ...(i)23x+32y=8134x+9y6=253 4x+9y=  50             ...(ii)Here, we observe that the coefficients of x and y in the first equation are interchanged in the second equation.Adding these two equations, we get:          9x+4y=  80              4x+ 9y=  50          13x+13y=130    x+y=10                ...(iii)Subtracting eq (ii) from (i), we get:         9x+4y=  80                 4x+9y=  50       -     -    -                 5x-5y  =30             ...(iv)  x-y=6        From (iii) &(iv), we get:  x+y=10 and    x-y=6Adding (iii) and (iv), we get:             x+y=  10                 x-y=    6           2x     = 16 x=8Substituting  x=8 in eq (iii), we get: 8+y=10  y=2Hence, x=8 and y=2 is the solution of the given equations .

Mathematics
Mathematics (Algebra)
Standard IX

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