How Do You Determine if an Ordered Pair is a Solution to a Linear Inequality?

≤ means 'less than or equal to'
To see if an ordered pair is a solution to an inequality, plug the ordered pair in and simplify
(2,-6) and (-7,4) are (x,y) ordered pairs
Plugging in (2,-6) gave us a true statement, which means that (2,-6) is a solution!
(-7,4) gave us a false statement after we plugged it in, so that ordered pair is not a solution!

1. (2,-6) is an (x,y) ordered pair
1. To see if an ordered pair is a solution to an inequality, plug the ordered pair in and simplify
2. x=2 and y=-6 so we get -6≤3(2)+6
1. Multiply the 3 and 2 together to simplify the right hand side of the inequality
2. -6≤3(2)+6 becomes -6≤6+6
1. Add 6+6 on the right hand side of the inequality
2. -6≤6+6 becomes -6≤12
1. If we got a false statement at the end, we would know that (2,-6) is not a solution to y≤3x+6
2. -6≤12 is a true statement because -6 is less than 12
1. (-7,4) is an (x,y) ordered pair
1. You can figure out if an ordered pair is a solution to a linear inequality by plugging it in and simplifying
2. x=-7 and y=4 so we get 4≤3(-7)+6
1. Multiply the 3 and -7 together to simplify the right hand side of the inequality
2. 4≤3(-7)+6 becomes 4≤-21+6
1. Add -21+6 on the right hand side of the inequality
2. 4≤-21+6 becomes 4≤-15
1. If we got a true statement at the end, we would know that (-7,4) is a solution to y≤3x+6
2. 4≤-15 is a false statement because 4 is not less than or equal to -15, it's larger!

Determine whether the following ordered pairs are solutions of y ≤ 3x + 6: a. ( 2, -6) b. ( -7, 4)