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| 1. |
mx-ny=m^2+n^2x+y=2nSolve by cross- multiplication method |
| Answer» Given equations aremx - ny = m2 + n2 .................(i)x + y = 2m ....................(ii)Herea1 = m, b1 = -n, c1 = -(m2 + n2)a2 = 1, b2 = 1, c2 = -(2m)By cross multiplication method{tex}\\frac{x}{{{{( 2mn + m^2 + n^2)} }}} = \\frac{{ - y}}{{ - {2m^2} + m^2 + n^2 }} = \\frac{1}{{m + n}}{/tex}{tex}\\frac{x}{{{{(m + n)}^2}}} = \\frac{{ - y}}{{ - {m^2} + {n^2}}} = \\frac{1}{{m + n}}{/tex}Now, {tex}\\frac{x}{{{{(m + n)}^2}}} = \\frac{1}{{m + n}} {/tex}{tex}⇒ x = m + n{/tex}And, {tex}\\frac{{ - y}}{{ - {m^2} + {n^2}}} = \\frac{1}{{m + n}}{/tex}{tex} ⇒ y = m - n{/tex}The solutions of the given pair of equations are x = m + n and y = m - n. | |