Question

Which system of linear inequalities has the point (2, 1) in its solution set?

Answer 1

You haven't provided the choices, therefore, I cannot provide an exact answer. However, I will help you with the concept.

For an order pair to be a solution to a system of equations, it has to satisfy BOTH equations. If it satisfies only one equation of the system or satisfy neither of the equations, the, it is not a solutions

Examples:
System 1:
x = y + 1
2x + 3y = 7
Let's check (2,1)
2 = 1 + 1 ........> equation 1 is satisfied
2(2) + 3(1) = 7 ......> equation 2 is satisfied
(2,1) is a solution to this system

System 2:
y = x + 3
y = x - 1
Let's check (2,1):
1 ≠ 2 + 3 ........> equation 1 isn't satisfied
1 = 2 - 1 ..........> equation 2 is satisfied
(2,1) isn't a solution to this system

System 3:
2y = 9 - 3x
3x + 2y = 9
Let's ceck (2,1):
2(1) ≠ 9 - 3(2) ..........> equation 1 isn't satisfied
3(2) + 2(1) ≠ 9 .........> equation 2 isn't satisfied
(2,1) isn't a solution to this system

Based on the above, all you have to do is substitute with (2,1) in the system you have and pick the one where both equations are satisfied

Hope this helps :)