Name _____________________ Per_____
4.7 GRAPHING SYSTEMS OF INEQUALITIES
WHAT “IS” A SOLUTION?
Determine all possible solution(s) to each of the following:
1. y = 4x – 2
2. y ≤ 4x-2
3. y = 4x-2
y = x+1
4. y ≤4x-2
y ≤ x+1
5. What “is” a solution? _____________________________________________________________________________
For example:
Test the following points to determine if they are solutions to the system of inequalities.
6. System of Inequalities:
a.
Is (0,0) a solution? yes/no
Show why or why not:
b. Is (2,1) a solution? yes/no
Show why or why not:
c. Is (4,-2) a solution? yes/no
Show why or why not:
b. Is (-4,1) a solution? yes/no
Show why or why not:
c. Is (3,1) a solution? yes/no
Show why or why not:
b. Is (0,0) a solution? yes/no
Show why or why not:
c. Is (1,-3) a solution? yes/no
Show why or why not:
7. System of Inequalities:
b.
Is (0,0) a solution? yes/no
Show why or why not:
8. System of Inequalities:
c.
Is (2,0) a solution? yes/no
Show why or why not:
HOW TO GRAPH SYSTEMS OF INEQUALITIES
Graph each inequality. Identify the half-plane where the solutions lie for each equation. Shade the region where BOTH
solutions meet.
CHANGE TO Y<MX+B FORMAT, THEN GRAPH
Change to y<mx+b format, then graph the system of inequalities.
18.
2y > x - 4
19. 6y ≤ -18x - 18
3y ≥ 9x + 9
4y > -12x – 4
20. y – 5x ≤-3
2y + 2x < 6
GRAPHING SYSTEMS OF INEQUALITIES (4 INEQUALITIES) – BOUNDED REGIONS
Graph each system of inequalities. Identify the points of intersections.
21.
22.
23.
PROBLEMS IN CONTEXT
Write a system of inequalities to match each situation.
24.
25.
26.
27.
ANSWER KEY (Check your answers!)
5) a solution is an (x,y) pair that makes the equation/inequality a true statement
6) a. yes
b. no c. no
7) a. no
b. yes c. no
8) a. no
b. no c. yes
21)
22)
23)
25)
26)
27)