Question

State the coordinates of a point in the solution set. y, is less than or equal to, x, plus, 2 y≤x+2 y, is less than, minus, 2, x, minus, 1 y<−2x−1

Answer 1

To find the coordinates of a point in the solution set, substitute different values for x and calculate the corresponding y values using the given inequalities. Three possible points in the solution set are (0,2), (1,-3), and (-1,1).

Step-by-step explanation:

To find the coordinates of a point in the solution set, we need to identify the values of x and y that satisfy all three inequalities.

Starting with the first inequality, y ≤ x + 2, we can choose any value for x and calculate the corresponding y value. For example, if we let x = 0, then y ≤ 2. So, one possible point is (0,2).

Moving on to the second inequality, y < -2x - 1, we can again choose any value for x and calculate y. Let's say x = 1, then y < -2(1) - 1 = -3. So, another possible point is (1,-3).

Finally, for the third inequality, y < -2x - 1, let's choose x = -1. Substituting this into the inequality, we get y < -2(-1) - 1 = 1. Therefore, another possible point is (-1,1).

So, there are multiple points in the solution set. The coordinates of three such points are (0,2), (1,-3), and (-1,1).