Question

(a+2b)x + (2a-b)y = 2
(a-2b)x + (2a+b)y = 3

by elimination method...

best answer will be marked as brainliest

Answer 1

hope it help u a lot

Answer 2

Answer:  The required solution is

$x=\dfrac{-2a+5b}{10ab},~~~y=\dfrac{a+10b}{10ab}.$

Step-by-step explanation:  We are given to solve the following system of equations by elimination method :

$(a+2b)x+(2a-b)y=2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\(a-2b)x+(2a+b)y=3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Multiplying equation (i) by (a - 2b) and equation (ii) by (a + 2b), we have

$(a+2b)(a-2b)x+(2a-b)(a-2b)y=2(a-2b)\\\\\Rightarrow (a^2-4b^2)x+(2a^2-5ab+2b^2)y=2a-4b~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

and

$(a-2b)(a+2b)x+(2a+b)(a+2b)y=3(a+2b)\\\\\Rightarrow (a^2-4b^2)x+(2a^2+5ab+2b^2)y=3a+6b~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)$

Subtracting equation (iii) from equation (iv), we get

$(a^2-4b^2)x+(2a^2+5ab+2b^2)y-(a^2-4b^2)x-(2a^2-5ab+2b^2)y=(3a+6b)-(2a-4b)\\\\\Rightarrow 10aby=a+10b\\\\\Rightarrow y=\dfrac{a+10b}{10ab}.$

Substituting the value of y in equation (i), we get

$(a+2b)x+(2a-b)\times\dfrac{a+10b}{10ab}=2\\\\\\\Rightarrow (a+2b)x+\dfrac{2a^2+19ab-10b^2}{10ab}=2\\\\\\\Rightarrow (a+2b)x=2-\dfrac{2a^2+19ab-10b^2}{10ab}\\\\\\\Rightarrow x=\dfrac{-2a^2+ab+10b^2}{10ab(a+2b)}\\\\\\\Rightarrow x=\dfrac{-2a^2+5ab-4ab+10b^2}{10ab(a+2b)}\\\\\\\Rightarrow x=\dfrac{a(-2a+5b)+2b(-2a+5b)}{10ab(a+2b)}\\\\\\\Rightarrow x=\dfrac{(a+2b)(-2a+5b)}{10ab(a+2b)}\\\\\\\Rightarrow x=\dfrac{-2a+5b}{10ab}.$

Thus, the required solution is

$x=\dfrac{-2a+5b}{10ab},~~~y=\dfrac{a+10b}{10ab}.$