mathleaks.com mathleaks.com Start chapters home Start History history History expand_more
{{ item.displayTitle }}
navigate_next
No history yet!
Progress & Statistics equalizer Progress expand_more
Student
navigate_next
Teacher
navigate_next
Expand menu menu_open Minimize
{{ filterOption.label }}
{{ item.displayTitle }}
{{ item.subject.displayTitle }}
arrow_forward
No results
{{ searchError }}
search
menu_open home
{{ courseTrack.displayTitle }}
{{ statistics.percent }}% Sign in to view progress
{{ printedBook.courseTrack.name }} {{ printedBook.name }}
search Use offline Tools apps
Login account_circle menu_open

Describing Solutions to Systems of Linear Equations

Describing Solutions to Systems of Linear Equations 1.9 - Solution

arrow_back Return to Describing Solutions to Systems of Linear Equations
a

We will use an example to answer this question. Let's consider a system of linear equations. Note that both the and the variables have the same coefficient in both equations. Thus, in order to use the elimination method, we will subtract Equation (II) from Equation (I). We arrived to a true statement. Its truthfulness does not depend on any variable. Thus, any value for and will satisfy the statement. This happens when the two lines are coincidental and then the system has infinitely many solutions.

b
To answer this question, we will consider another example. In this system the variable has opposite coefficients. Therefore, we will add the equations to eliminate it. We found that To find the value of the variable, we will substitute for in Equation (II) and solve the resulting equation.
We found that the solution of the system is Therefore, there is only one solution. Note that whenever we arrive to a concrete solution for each of the variables, the system has one solution.
c

Finally, to answer this question, we will use a third example. In this example the and the variables have opposite coefficients. Therefore, to solve the system, we will add the equations. Since we know that we have a arrived at a false statement. There are no values for and that satisfy it. Thus, the system has no solution. This means the lines do not intersect. Every time we arrive to a false statement, the system has no solution.