Linear system: real-life situations and solutions
Objectives
Student will be able to:
develop and write systems of linear equations to represent real-life situations.
solve systems of linear equations by graphing using technology when appropriate.
determine whether a system of linear equations has one solution, no solution, or infinitely many solutions by graphing and interpret the solution in a real-life situation.
Introduction
When two lines are graphed on the same coordinate grid, the lines will be intersecting, parallel, or the same line.
These linear equations, which share the same variables, are called a system of equations. The solution to the system of equations is the point of intersection of the two lines.
We can develop and write a system of equations to model real-life problems in which several relationships exist between the same set of variables.
Exercises
Choose the correct solution to each system of linear equations. Use a graphing calculator to solve.
1.
Determine the solution to the following linear system.
a.
b.
c.
d.
d.
1
.
Correct
Incorrect
Not Assigned
2.
Which answer represents the point of intersection for the following system of linear equations?
a.
b.
c.
d.
b.
2
.
Correct
Incorrect
Not Assigned
3.
The system of linear equations below intersects at which point?
a.
b.
c.
d.
a.
3
.
Correct
Incorrect
Not Assigned
4.
Choose the solution for the following linear system.
a.
b.
c.
d.
c.
4
.
Correct
Incorrect
Not Assigned
5.
The sum of two numbers is 6. Their difference is –2. Which ordered pair represents the two numbers?
a.
b.
c.
d.
c.
5
.
Correct
Incorrect
Not Assigned
Complete the exercises. Show all work.
6.
Solve the linear system. Use a graphing calculator or the blank graph provided.
Check student's work.
6
.
Correct
Incorrect
Not Assigned
7.
The sum of two numbers is 14. Two times the smaller number minus the larger number is 4. Write and solve a system of equations to determine the two numbers. Use a graphing calculator to solve.
The system of equations:
(variables may vary)
The numbers are 6 and 8.
Check student's work.
7
.
Correct
Incorrect
Not Assigned
8.
The ticket prices for the late movie are $8 for adults and $5 for children. If a group of 11 people purchased tickets for a total of $67, how many adults and how many children attended the movie?
Four adults and seven children attended the movie.
Check student's work.
8
.
Correct
Incorrect
Not Assigned