Answer:
Part a) The system of linear inequalities is
y\geq 5y≥5
4x+10y\leq 1004x+10y≤100
Part b) The graph in the attached figure
Part c) A solution could be (5,7) (see the explanation)
Step-by-step explanation:
The complete question is
You are buying plants and soil for your garden. The soil cost 4.00 dollars per bag and the plants cost 10.00 each. You want to buy at least 5 plants and can spend no more than10.00each.Youwanttobuyatleast5plantsandcanspendnomorethan100
a) write a system of linear inequalities to model the situation
b) Graph the system of linear inequalities
c) Identify and interpret a solution to the system
Part a) write a system of linear inequalities to model the situation
Let
x -----> the number of bags of soil
y ----> number of plants
we know that
The word "at least" means "greater than or equal"
y\geq 5y≥5 ----> inequality A
The word "no more" means "less than or equal"
4x+10y\leq 1004x+10y≤100 ----> inequality B
Part b) Graph the system of linear inequalities
we have
y\geq 5y≥5 ----> inequality A
4x+10y\leq 1004x+10y≤100 ----> inequality B
using a graphing tool
the solution is the triangular shaded area
see the attached figure
Part c) Identify and interpret a solution to the system
we know that
If a ordered pair is a solution to the system, then the ordered pair must lie on the shaded area of the solution
i take the point (5,7)
the point (5,7) lie on the shaded area of the solution
so
is a solution of the system
That means ----> You are buying 5 bags of soil and 7 plants for your garden
Verify the solution
Remember
If a ordered pair is a solution to the system, then the ordered pair must satisfy both inequalities
Verify inequality A
7\geq 57≥5 ----> is true
so
The ordered pair (5,7) satisfy inequality A
Verify inequality B
4(5)+10(7)\leq 1004(5)+10(7)≤100
90\leq 10090≤100 ---> is true
so
The ordered pair (5,7) satisfy inequality B
therefore
The ordered pair (5,7) is a solution to the system
