Solving System of Inequality
Lesson date Wednesday Feb. 25,2015
Objective
Linear Inequality
A Linear Inequality describes a region of the coordinate plane that has a boundary line. the solution of an inequality are the coordinates of the points that make the inequality true.
Example (1) Graph the system of Inequalities
y > -x -2 (inequality 1)
y ≤ 3x +6
first: graph both inequalities in the same coordinate plane. the graph of the system is the intersection of the two half planes, which is shown as the darker shade of blue.
check:
choose a point in the dark blue region, such as (0,1). To check this solution, substitute 0 for x and 1 for y into each inequality.
1> 0-2 1≤ 0+6
1> -1 true 1≤6 true
Eample (2) Which order pair is a solution of the system
a) (1,-1)
b) (4,1)
c) (2,0)
d) ( 3, 2)
To check this solutions, substitute by the value f x for x and the value of y for y into each inequality.
Choice (a) (1,-1)
2x- y≤ 5 (inequality 1) and X +2y >2 (inequality 2)
2(1)- (-1)≤ 5 and 1 +2(-1) >2
2+1 ≤ 5 and 1 -2 >2
3 ≤ 5 true and -1 >2 false
so the choice A is not a solution
Choice (b) (4,1)
2x- y≤ 5 (inequality 1) and X +2y >2 (inequality 2)
2(4)- (1)≤ 5 and 4 +2(1) >2
7 ≤ 5 False and 6 >2 True
so the choice B is not a solution
Choice (c) (2,0)
2x- y≤ 5 (inequality 1) and X +2y >2 (inequality 2)
2(2)- (0)≤ 5 and 2 +2(0) >2
4 ≤ 5 true and 2 >2 False
so the choice c is not a solution
Choice (d) (3,2)
2x- y≤ 5 (inequality 1) and X +2y >2 (inequality 2)
2(3)- (2)≤ 5 and 3 +2(2) >2
4 ≤ 5 true and 7 >2 True
so the choice d is a solution
Exapmle (3) Think and share your thoughts on the comment section
Fishing Limits:
you are fishing in a marina for surfperch and rockfish, which are two species of bottom fish. Gaming laws in the marina allow you to catch no more than 15 surfperch per day, no more than 10 rockfish per day, and no more than 15 total bottomfish per day.
a) Write and graph a system of inequalities that models the situation.
b) use the graph to determine whether you can catch 11 surperch and 9 rockfish in one day.