Answer
\[x=2,\ y=4\]
Work Step by Step
Add the given equations from both RHS and LHS as follows:
\[\begin{align}
& \underline{\begin{align}
& x+y=6 \\
& x-y=-2 \\
\end{align}} \\
& 2x\ \ \ \ =4 \\
& \ \ \ \ \ x=2 \\
\end{align}\]
Put \[x=2\]in\[x+y=6\], to get:
\[\begin{align}
& 2+y=6 \\
& y=4
\end{align}\]
Put\[x=2\]and \[y=4\]in any of the given equations to check the solution:
\[\begin{align}
& 2-\left( 4 \right)=-2 \\
& 2-4=-2 \\
& -2=-2
\end{align}\]
Since RHS\[=\]LHS, it implies the solution is correct.
Similarly check its solution by putting values of x and y in the x + y = 6 too:
2 + 4 = 6
6 = 6
RHS = LHS , so it has been verified that x = 2 and y = 4 is the solution of this system of equations.
