Systems of Equations Exercises

Example 1

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.

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.

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?

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.

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.

Systems of Equations Exercises

Example 1

Example 2

Example 3

Example 4

Example 5

Tired of ads?