Mathematics 2000 JAMB Past Questions - Question 17: The solution of the simultaneous inequalities 2x-2 ≤ y and 2y-2 ≤ x is represented by

Correct Answer

B

Explanation

To find the solution to the simultaneous inequalities 2x - 2 ≤ y and 2y - 2 ≤ x, you can graph both inequalities and find the region where they overlap.First, let's graph the inequalities one by one:2x - 2 ≤ y: Subtract 2x from both sides: -2 ≤ y - 2x. Add 2 to both sides: y ≥ -2x + 2.This inequality represents a line with a slope of -2 and a y-intercept of 2. It is the boundary of the solution region.2y - 2 ≤ x: Add 2 to both sides: 2y ≤ x + 2. Divide both sides by 2: y ≤ 0.5x + 1.This inequality represents another line with a slope of 0.5 and a y-intercept of 1. It is also the boundary of the solution region.Now, let's graph both of these lines on the same coordinate system:To find the overlapping region, consider the area below the line y = -2x + 2 (including the line itself) and below the line y = 0.5x + 1 (including the line itself). The overlapping region is the shaded area between the two lines:bashCopy code ^ | /|\ | / | \ | / | \ | / | \ |/_____a_____\________> The shaded area marked as 'a' in the graph represents the solution to the simultaneous inequalities 2x - 2 ≤ y and 2y - 2 ≤ x. Any point within or on the shaded region satisfies both inequalities.So, the solution to the simultaneous inequalities is the shaded region between the two lines.