Question

solve the simultaneous equation in two variables by the method of comparison.. ​

Answer 1

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \boxed{\boxed { \huge \mathcal\red{ solution}}}}$

From the first equation

$\frac{1}{3}(x-y)=\frac{1}{4}(y-1)\\</p><p>\implies 4(x-y)=3(y-1)\\</p><p>\implies 4x-4y=3y-3\\</p><p>\implies 4x=3y+4y-3\\ </p><p>\implies 4x=7y-3\\</p><p>\implies \boxed{12x=21y-9}............(i)$

From the second equation

$\frac{1}{7}(4x-5y)=(x-7)\\</p><p>\implies (4x-5y)=7(x-7)\\</p><p>\implies 4x=7x-49+5y\\</p><p>\implies 4x-7x=5y-49\\ </p><p>\implies -3x=5y-49\\</p><p>\implies 3x=49-5y\\</p><p>\implies \boxed{12x=196-20y}......(ii)$

Comparing equations (i)&(ii)...

$\implies 21y-9=196-20y\\ \implies 21y+20y=196+9\\ \implies 41y=205\\ \implies 41y=205\\ y=\frac{\cancel{205}}{\cancel{41}}\\</p><p>\implies \boxed{\bf\red{y=5}}$

Now putting the value y=5 in equation (i)

$\implies 12x=21(5)-9\\</p><p>\implies x=\frac{96}{12}\\</p><p>\implies \boxed{\bf\red{x=8}}$

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