Respuesta :
To find the point that satisfies both inequalities, we need to locate the area where the shaded regions of the graphs overlap.
Let's analyze the given inequalities and their corresponding graphs:
1. Inequality: y < -3/2x + 2
Graph: A line with a slope of -3/2 passing through the point (0, 2).
2. Inequality: y < 2x + 6
Graph: A line with a slope of 2 passing through the point (0, 6).
To determine the point that satisfies both inequalities, we need to identify the overlapping region. Looking at the two graphs, the shaded region of the first inequality is below the line, and the shaded region of the second inequality is also below its line.
By imagining the shading, we can see that the overlapping region would be below both lines. So, the point that satisfies both inequalities should have a y-coordinate that is less than the y-coordinates of both lines.
From the given options, the only point that satisfies both inequalities is (-1, 0). If you plot this point on the graphs, you will see that it falls below both lines and within the overlapping region.
Therefore, the point (-1, 0) satisfies both inequalities.
