Which of the points shown on the graph is a solution to the simultaneous inequalities y>3x+1
and y≤2x+5
? Write the x-value first and the y-value second.
To find the solution to the simultaneous inequalities, we need to identify the points on the graph that satisfy both conditions simultaneously.
The points on the graph that are above the line y = 3x + 1 represent the solutions to the inequality y > 3x + 1. These points are located above the line and are not on the line itself.
The points on the graph that are on or below the line y = 2x + 5 represent the solutions to the inequality y ≤ 2x + 5. These points are located on or below the line.
To find the solution to the simultaneous inequalities, we need to find the overlapping area on the graph where the points satisfy both conditions. In other words, we need to find the points that are both above the line y = 3x + 1 and on or below the line y = 2x + 5.
Looking at the graph, we see that the overlapping area occurs between x = 1 and x = 3. Within this range, the overlapping points are (1, 4) and (3, 7).
Therefore, the solutions to the simultaneous inequalities y > 3x + 1 and y ≤ 2x + 5 are (1, 4) and (3, 7).