Answer: No, (3,4) is not a solution of the system.
Step-by-step explanation:
Let's start with y ≤ 2x.
(3,4) is an ordered pair following (x,y), meaning that x=3 and y=4. We can substitute the values of x and y into the inequalities above.
y ≤ 2x Original inequality
4 ≤ 2(3) Substitute x and y values
4 ≤ 6 ✓ Simplify
Yes, it's true that 4 ≤ 6, so we've confirmed that (3,4) works in the first part of the system. Now for y > x + 4:
y > x + 4 Original inequality
4 > 3 + 4 Substitute x and y
4 > 7 ❌ Simplify
Both inequalities have to be true for the ordered pair to be a solution of the system. (3,4) works for the first inequality, but not the second (since 4 is NOT greater than 7), and so it is not a solution of the system.
