8/(2x+3y) +21/(2x-3y)=11; 5/(2x+3y) +7/(2x-3y)=-6;

1.	8/(2x+3y) +21/(2x-3y)=11; 5/(2x+3y) +7/(2x-3y)=-6;
Answer» Given equations are{tex}\\frac{8}{2x - 3y}{/tex}\xa0+\xa0{tex}\\frac{21}{2x + 3y}{/tex}\xa0= 11...(i){tex}\\frac{5}{2x - 3y}{/tex}\xa0+\xa0{tex}\\frac{7}{2x + 3y}{/tex}\xa0= 6 ....(ii)Putting\xa0{tex}\\frac{1}{2x - 3y}{/tex}\xa0= A and\xa0{tex}\\frac{1}{2x + 3y}{/tex}\xa0= B in equation (i) & (ii) so that we may get the pair of linear equations in variables A & B as following :-8A + 21B = 11 ...(iii). and 5A + 7B = 6...(iv)Multiplying eq. (iv) by 3 & then subtracting eq. (iii) from it , we get ;{tex}\\Rightarrow{/tex}\xa0A = 1\xa0Substituting A = 1 in eq. (iii) ,8\xa0{tex}{/tex}× 1 + 21B = 11{tex}\\Rightarrow{/tex}\xa021B = 3{tex}\\Rightarrow{/tex}\xa0B =\xa0{tex}\\frac{1}{7}{/tex}Since, A = 1{tex}\\Rightarrow{/tex}\xa0{tex}\\frac{1}{2x - 3y}{/tex}\xa0= 1{tex}\\Rightarrow{/tex}\xa02x - 3y = 1...(vi)Where B =\xa0{tex}\\frac{1}{7}{/tex}{tex}\\Rightarrow{/tex}{tex}\\frac{1}{2x + 3y}{/tex}\xa0=\xa0{tex}\\frac{1}{7}{/tex}{tex}\\Rightarrow{/tex}2x + 3y = 7...(vii)Adding (vi) and (vii), we get{tex}\\Rightarrow{/tex}x = 2Substituting x = 2 in eq.(vi),\xa02{tex}{/tex}× 2 - 3y = 1{tex}\\Rightarrow{/tex}\xa0-3y = -3{tex}\\Rightarrow{/tex}\xa0y = 1{tex}\\therefore{/tex}\xa0x = 2, y = 1.

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