To find the solution to the simultaneous inequalities, we need to find the region that satisfies both inequalities.
First, let's graph the inequality y > 1/2x + 5:
- Plot the y-intercept at (0, 5).
- Identify the slope of 1/2, which means for every 1 unit increase in x, y increases by 1/2 units.
- Plot another point using the slope from the y-intercept, such as (2, 6).
Next, let's graph the inequality y < -2x + 1:
- Plot the y-intercept at (0, 1).
- Identify the slope of -2, which means for every 1 unit increase in x, y decreases by 2 units.
- Plot another point using the slope from the y-intercept, such as (1, -1).
The two lines intersect at the point (2, 6). Since this point is in the region satisfying both inequalities, it is a solution to the simultaneous inequalities.
Therefore, the correct point that shows a solution to the simultaneous inequalities is (2, 6).
Which of the following points shows a solution to the simultaneous inequalities y>1/2x+5 and y<−2x+1 ?
1 answer