Math, asked by abhaysankhla, 1 year ago

solve the equation by substitution method

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Answered by hukam0685
5

ax( \frac{a  + b - a + b}{ {a}^{2}  -  {b}^{2} } ) + by( \frac{b + a - b + a}{ {b}^{2} -  {a}^{2}  } ) = 2 \\  =  \frac{2bax}{ {a}^{2}  -  {b}^{2} }  +  \frac{2aby}{ {b}^{2}  -  {a}^{2} }  = 2
 \frac{2abx}{ {a}^{2} -  {b}^{2}  }  -  \frac{2aby}{ {a}^{2} -  {b}^{2}  }  = 2 \\ abx - aby =  {a}^{2}  - {b}^{2}
now substitute value of x from eq2 into eq2
x =  \frac{(a + b) - ay}{b}
ab ( \frac{(a + b) - 2y}{a} ) - aby =  {a}^{2}  -  {b}^{2}  \\ ab +  {b}^{2}  - 2by - aby =  {a}^{2}  -  {b}^{2}  \\  - (2b + ab)y =  {a}^{2}  -  {b}^{2}  -  {b}^{2}  - ab \\ y =  \frac{ {a}^{2} - 2 {b}^{2}  - ab }{ - (2b + ab)}
put the value of y in eq1


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