PYQ NEET- Linear Inequality In Two Variables

Question 1:

2x + 5y ≤ 10, x + 3y ≤ 7, x ≥ 0, y ≥ 0.

The first equation is a line with slope -2/5 and y-intercept 2. The second equation is a line with slope -1/3 and y-intercept 7/3. The two lines intersect at (2, 1).

The region that satisfies all of the constraints is the area below the line 2x + 5y ≤ 10 and above the line x + 3y ≥ 7. This region is shaded in the following figure.

The vertices of the feasible region are (0, 0), (2, 1), (3, 2), and (4, 0). The maximum value of y is 2, which occurs at (2, 1).

Therefore, the solution to the problem is x ≤ 2 and y ≤ 2.

Question 2:

3x + 2y ≤ 1