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Example 5.53 from Elementary Algebra, 5.6 Graphing Systems of Linear Inequalities
Graphing Systems of Linear Inequalities: example 5.53
Solve the system by graphing.
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
Solution
Graph x − y > 3, by graphing x − y = 3 and
testing a point.
The intercepts are x = 3 and y = −3 and the boundary
line will be dashed.
Test (0, 0). It makes the inequality false. So,
shade the side that does not contain (0, 0) red.Graph by graphing
using the slope and y−intercept
b = 4. The boundary line will be dashed.
Test (0, 0). It makes the inequality true, so shade the side that contains (0, 0) blue.
Choose a test point in the solution and verify that it is a solution to both inequalities.The point of intersection of the two lines is not included as both boundary lines were dashed. The solution is the area shaded twice which is the darker-shaded region.
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
Solve the system by graphing.
How did it go?