Final answer:
The ordered pairs that are solutions to the inequality 2y - x ≤ -6 are (1, -4), (2, -2), and (0, -3), as they satisfy the inequality when their values are substituted into the equation.
Step-by-step explanation:
To find which ordered pairs are solutions to the inequality 2y - x ≤ -6, we must plug in the x and y values from each ordered pair into the inequality to see if the statement holds true. Here is how we test each ordered pair:
- For (1, -4), substitute x = 1 and y = -4: 2(-4) - (1) = -8 - 1 = -9, which is less than -6. So, (1, -4) is a solution.
- For (2, -2), substitute x = 2 and y = -2: 2(-2) - (2) = -4 - 2 = -6, which is equal to -6. So, (2, -2) is a solution.
- For (0, -3), substitute x = 0 and y = -3: 2(-3) - (0) = -6 - 0 = -6, which is equal to -6. So, (0, -3) is a solution.
- For (6, 1), substitute x = 6 and y = 1: 2(1) - (6) = 2 - 6 = -4, which is greater than -6. Therefore, (6, 1) is not a solution.
- For (-3, 0), substitute x = -3 and y = 0: 2(0) - (-3) = 0 + 3 = 3, which is greater than -6. Therefore, (-3, 0) is not a solution.
Therefore, the ordered pairs that are solutions to the inequality are (1, -4), (2, -2), and (0, -3).