Verified Answer :

\(\left \{ {{x+y=3\:(I)} \atop {x-y=1\:(II)}} \right.\)

by elemination

\(\left \{ {{x+\diagup\!\!\!\!y=3} \atop {x-\diagup\!\!\!\!y=1}} \right.\)
\(\left \{ {{x=3} \atop {x=1}} \right.\)
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\(2x = 4\)
\(x = \frac{4}{2}\)
\(\boxed{x = 2}\)


Replace the found value of "x", to find the value of "y"
\(x+y=3\:(I)\)
\(2 + y = 3\)
\(y = 3 - 2\)
\(\boxed{y = 1}\)

Answer:
X = 2
Y = 1