Question

systems of linear equations/inequalities exam
name:
partial credit is only considered if work is shown
block: 1 2 3 4 5 6 7 8

1. is this ordered pair (dot) a solution to this system? (a.ei.2)

a. yes or no (10 points)
b. why? or why not? (10 points)
desmos | virginia | standards of learning version

1. ( y > 3x + 4 )
2. ( y leq -2x - 2 )
3. ( (-2, -2) ) (label option)

(graph showing the system of inequalities and the point (-2, -2))

Explanation:

Step1: Check first inequality

Substitute \( x = -2 \), \( y = -2 \) into \( y > 3x + 4 \).
Calculate \( 3x + 4 = 3(-2) + 4 = -6 + 4 = -2 \).
So we check if \( -2 > -2 \). This is false (since \( -2 = -2 \), not greater).

Step2: Conclusion

A solution to the system must satisfy both inequalities. Since the ordered pair fails the first inequality (\( y > 3x + 4 \)), it is not a solution.

Answer:

a. No
b. The ordered pair \((-2, -2)\) does not satisfy \( y > 3x + 4 \) (as \( -2 = 3(-2) + 4 \), so \( -2
ot> -2 \)), so it is not a solution to the system.