Determine whether the ordered pair is a solution of the given system.
(3,11);
y
> 2x + 2 y
< 4x + 1
Is (3,11) a solution of the given system?
To determine whether the ordered pair is a solution of the given system, we substitute the values of x and y from the ordered pair into the equations and check if the equations are satisfied.
For the first equation, y > 2x + 2, we substitute x = 3 and y = 11:
11 > 2(3) + 2
11 > 6 + 2
11 > 8
The inequality 11 > 8 is true, so the ordered pair satisfies the first equation.
For the second equation, y < 4x + 1, we substitute x = 3 and y = 11:
11 < 4(3) + 1
11 < 12 + 1
11 < 13
The inequality 11 < 13 is true, so the ordered pair satisfies the second equation.
Since the ordered pair satisfies both equations, it is a solution of the given system.