y ≥ 2x - 6
y < 5x + 2
Describe how you could determine whether((5, 2) is a solution to the system of inequalitie
To determine whether the point (5, 2) is a solution to the system of inequalities, you need to substitute the values of x and y into each inequality and then check if the resulting inequality statements are true or false.
1) y ≥ 2x - 6:
Substituting x = 5 and y = 2 into the inequality gives:
2 ≥ 2(5) - 6
2 ≥ 10 - 6
2 ≥ 4
Since 2 is not greater than or equal to 4, the inequality is false.
2) y < 5x + 2:
Substituting x = 5 and y = 2 into the inequality gives:
2 < 5(5) + 2
2 < 25 + 2
2 < 27
Since 2 is less than 27, the inequality is true.
Based on the results:
- The point (5, 2) satisfies the inequality y < 5x + 2.
- The point (5, 2) does not satisfy the inequality y ≥ 2x - 6.
Therefore, (5, 2) is not a solution to the system of inequalities.