Question

If x+y =6; x - y=4 then find the value of x and y​

Answer 1

$\bold{Given :} \\ \\ = > x + y = 6 \\ = > x - y = 4 \\ \\ \bold{To \: find : } \\ \\ Value \: of \: x \: and \: y \\ \\ \bold{Method :} \\ \\ We \: are \: using \: \bold{ Elimination \: Method } \\ \\ \bold{Solution :} \\ \\ \implies \: x + y = 6 - - - (1) \\ \implies \: x - y = 4 - - - (2) \\ \\ Now \: add \: equation \: 1 \: and \: 2 : \\ \\ \implies \: x + y + x - y = 6 + 4 \\ \\ \implies \: x + \cancel{ y }+ x - \cancel{y }= 6 + 4 \: \\ \\ \implies \: 2x = 10 \\ \\ \implies \: x = \frac{10}{2} \\ \\ \implies \: x = \cancel\frac{10}{2} \\ \\ \implies \: \bold \blue{ x = 5} \\ \\ Now \: put \: value \: of \: x \: in \: equation \: 2 : \\ \\ \implies \: 5 - y = 4 \\ \\ \implies \: - y = 4 - 5 \\ \\ \implies - y = - 1 \\ \\ \implies \cancel{- }y = \cancel{ - }1 \\ \\ \implies \: \bold \red{y = 1} \\ \\ Therefore , \\ \\ </p><p></p><p>(1) \: Value \: of \: x = \bold \blue{5} \\ </p><p>(2) \: Value \: of \: y = \bold \red{1} \\ \\ \bold{Verification :} \\ \\ We \: can \: verify \: our \: answer \: by \: putting \: \\ values \: of \: x \: and \: y \: in equation \: 1 \: and \: 2 : \\ \\ (1) \: x + y = 6 \\ \\ \implies \: 5 + 1 = 6 \\ \\ \implies \: 6 = 6 \\ \\ \implies \: L.H.S = R.H.S \\ \\ </p><p>(2) \: x - y = 4 \\ \\ \implies \: 5 - 1 = 4 \\ \\ \implies \: 4 = 4 \\ \\ </p><p>L.H.S = R.H.S \\ \\ Therefore \: our \: answer \: is \: correct .</p><p></p><p>$