Solve the pair of linear equation37x+43y=123,43x+37y=117

1.	Solve the pair of linear equation37x+43y=123,43x+37y=117
Answer» The given equations are37x\xa0+ 43y = 123 ... (i)43x\xa0+ 37y = 117. ... (ii)Clearly, the coefficients of x\xa0and y in one equation are interchanged in the other.Adding (i) and (ii), we get(37x\xa0+ 43y) + (43x\xa0+ 37y) = 123 + 117(37 + 43)x+ (43 + 37)y = (123 +117){tex} \\Rightarrow{/tex}80x + 80y = 240{tex} \\Rightarrow{/tex}80(x\xa0+ y) = 240{tex} \\Rightarrow{/tex} x + y = 3 ....... (iii)Subtracting (i) from (ii), we get(37x\xa0+ 43y) - (43x\xa0+ 37y) = 123 - 1176x\xa0-\xa06y = -6{tex}\\Rightarrow{/tex}\xa06 (x - y) = -6{tex}\\Rightarrow{/tex}\xa0x\xa0- y = -1\xa0... (iv)Adding (iii) and (iv), we get(x + y) + (x - y) = 3 + (-1){tex}\\Rightarrow{/tex} x + y + x - y = 2{tex}\\Rightarrow{/tex} 2x\xa0= 2{tex}\\Rightarrow{/tex}\xa0x\xa0= 1.Subtracting (iv) from (iii), we get(x + y) - (x - y) = 3 - (-1){tex}\\Rightarrow{/tex}x + y - x + y = 4{tex}\\Rightarrow{/tex}2y = 4{tex}\\Rightarrow{/tex} y = 2.Hence, x\xa0= 1 and y = 2.

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