Solving systems of linear inequalities

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.