I will do #1 to show you how to solve these:
Equation 1: 2x + y = 6 → -1(2x + y = 6) → -2x - y = -6
Equation 2: 3x + y = 10 → 1(3x + y = 10) → 3x + y = 10
Now that one of the variables (y) has the same coefficient but opposite signs, we can add the two equations together to eliminate "y":
-2x - y = -6
+ 3x + y = 10
x = 4
Now that we know that x = 4, we can plug "4" in for "x" into Equation 1 or 2 to solve for "y". I am going to use Equation 1
Equation 1: 2x + y = 6 → 2(4) + y = 6 → 8 + y = 6 → y = -2
Answer: x=4, y=-2
NOTE: You can plug both x and y into the other equation to check that your answer is correct.