Question

for what value of k the equation X + Y is equals to K and x minus y is equals to 2 has unique solution​

Answer 1

$x + y = k.......(i) \\ x - y = 2 ........(ii)\\ x = 2 - y \\ put \: the \: value \: of \: x \: in \: equation \: (i) \\ 2 - y + y = k \\ k = 2 \\ hence \: again \: put \: the \: value \: of \: k \: in \: eqution \: (i) \\ x + y = 2.....(iii) \\ now \: equating \: the \: equation \: (ii) \: and \: (iii) \\ x + y = 2 ......(iii)\\ x - y = 2......(ii) \\ 2x = 4 \\ x = 2 \\ put \: the \: value \: of \: x \: and \: k \: in \: equation \: (i) \\ 2 + y = 2 \\ y = 2 - 2 \\ y = 0 \\ hence \: (x = 2) \:( y = 0) \:( k = 2)$

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