Question

Now, you should see the graphs for two inequalities: 3x + y < 9 and 3x - y < 9. Identify an ordered pair point that is a solution to both 3x + y < 9 and 3x - y < 9.

a) (1, 4)
b) (2, 3)
c) (3, 2)
d) (4, 1)

Answer 1

The ordered pair that is a solution to both 3x + y < 9 and 3x - y < 9 is (1, 4).

Step-by-step explanation:

To find the ordered pair that is a solution to both inequalities, we need to find the points that satisfy both 3x + y < 9 and 3x - y < 9. Let's check each given option:

• Option (a) (1, 4): For 3x + y < 9: 3(1) + 4 = 7 < 9 (true). For 3x - y < 9: 3(1) - 4 = -1 < 9 (true). So, (1, 4) satisfies both inequalities.
• Option (b) (2, 3): For 3x + y < 9: 3(2) + 3 = 9 < 9 (false). (2, 3) does not satisfy the first inequality, so it is not a solution.
• Option (c) (3, 2): For 3x + y < 9: 3(3) + 2 = 11 < 9 (false). (3, 2) does not satisfy the first inequality, so it is not a solution.
• Option (d) (4, 1): For 3x + y < 9: 3(4) + 1 = 13 < 9 (false). (4, 1) does not satisfy the first inequality, so it is not a solution.

Therefore, the only ordered pair that is a solution to both 3x + y < 9 and 3x - y < 9 is (1, 4) (option a).