To find the points that satisfy both inequalities, we need to find the overlapping region on the coordinate plane.
First, let's graph the lines represented by the inequalities:
y > 1/2x + 5
y < -2x + 1
Since both inequalities are strict (">" and "<"), the lines are not included in the solution. We will draw dashed lines to represent them.
The line y > 1/2x + 5 has a slope of 1/2 and a y-intercept of 5. We can plot a few points to help us draw the line.
When x = 0, y = 5. So we have the point (0, 5).
When x = 10, y = 5 + (1/2)(10) = 5 + 5 = 10. So we have the point (10, 10).
Drawing a dashed line through these points represents the inequality y > 1/2x + 5.
The line y < -2x + 1 has a slope of -2 and a y-intercept of 1. Again, we can plot a few points to help us draw the line.
When x = 0, y = 1. So we have the point (0, 1).
When x = 5, y = 1 + (-2)(5) = 1 + (-10) = -9. So we have the point (5, -9).
Drawing a dashed line through these points represents the inequality y < -2x + 1.
Now, we can identify the overlapping region between these lines. The shaded area represents the solution to both inequalities.
However, since we can't accurately draw a graph here, it's difficult to choose an exact point that satisfies both inequalities.
Therefore, we can say that there is no specific point from the given options that shows a solution to the simultaneous inequalities y > 1/2x + 5 and y < -2x + 1.
which of the following points shows a solution to the simultaneous inequalities y > 1/2x + 5 and y < -2x + 1
1 answer