Answer
$(3, 7)$ is the intersection point.
Work Step by Step
In order to check that the intersection point is correct, we plug in the supposed point, (3, 7), into both equations:
$x+y=10 \\ 3+7=10 \\ 10=10$
We now check the second equation:
$2x+y=13 \\ 2(3)+7 =13 \\13=13$
We see that the intersection point is correct as it is a solution to both equations.
