Graph y ≥ 100, state the boundary and find a point within the solution.
Hint
Graph y = 100 with a solid line, shade above and pick a point in the shaded region and write it's coordinate.
Answer
The boundary is y = 100. Any coordinate above and including the line will work as a point in the solution, for example (0, 150).
Example 2
Solve and state the boundary of:
2x + y > 1 x – y < -2
Hint
Solve each inequality for y. Graph each, shade, and find where the two shades overlap.
Answer
The solution is the intersection of the two graphs (dark green overlap) not including the boundaries of y = -2x + 1 and y = x + 2. You got this!
Example 3
Graph the solution of:
x2 + y2 ≤ 4 y ≥ 0
Hint
Graph the circle at (0, 0) with a radius of 2. Shade inside the circle. Graph the line y = 0 and shade above. Where do your two shaded regions overlap?
Answer
Example 4
Write the system of equations that has the solution of:
Hint
You will want to the left (and not including) x = 1, to the right and not including x = -1, above y = -1 and below y = 1.
Answer
y < 1
y > -1
x > -1
x < 1
Example 5
Solve this system of inequalities:
-x + 3y ≤ 8 2x + y ≥ 2 x ≥ 0 y ≥ 0 x ≤ 5
Hint
Solve the first two inequalities for y, then graph each line, shading above or below as you need. Make sure you shade to the left of x = 0 and to the right of x = 5.
Answer
The solution is the region with the darkest gray (the pentagon) in the middle of this picture.
