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| 1. |
(a-2b)X+(2a+b)=3 , (a+2b)X+(2a-b)y=2 |
| Answer» The given system of equations are :(a + 2b)x + (2a - b)y = 2So, (a + 2b)x + (2a - b)y - 2 = 0 ............(i)And (a - 2b) x + (2a + b) y = 3So, (a - 2b)x + (2a + b)y - 3 = 0 .........(ii)The given equations is in the form ofa1x + b1y + c1 = 0and a2x + b2y + c2 = 0So, we geta1 = a + 2b, b1 = 2a - b, c1 = -(2)a2 = a - 2b, b2 = 2a + b, c2 = (-3)By cross-multiplication method:{tex} \\frac{x}{{ - 2a + 5b}} = \\frac{y}{{a + 10b}} = \\frac{1}{{10ab}}{/tex}Now, {tex}\\frac{x}{{ - 2a + 5b}} = \\frac{1}{{10ab}} {/tex}{tex} ⇒ x = \\frac{{5b - 2a}}{{10ab}}{/tex}And {tex}\\frac{y}{{a + 10b}} = \\frac{1}{{10ab}} {/tex}{tex} ⇒ y = \\frac{{a + 10b}}{{10ab}}{/tex}The solution of the system of equations are {tex}x = \\frac{{5b - 2a}}{{10ab}}{/tex}\xa0and {tex}y = \\frac{{a + 10b}}{{10ab}}{/tex}\xa0respectively. | |