We are given some information about our and our friend's savings accounts. We will write a system of equations representing this situation. Let x represent the number of weeks that have passed and let y represent the total amount of money in our accounts.
Number of weeks passed - x Amount of money saved - y
At this moment, we have $ 50 in our savings account and our friend has $ 25 in their savings account. All of us plan to deposit $ 10 to our accounts each week. We can create a system of equations where the first equation represents our savings and the second one represents our friend's.
y= 10* x+ 50 & (I) y= 10* x+ 25 & (II)
Let's recall what we know about the number of solutions of a system of linear equations when we know their slope and y-intercepts.
Solutions of a System of Linear Equations
Slopes
y-Intercepts
Number of Solutions
Same
Same
Infinitely many solutions
Same
Different
No solution
Different
Different or the same
One solution
We can show those relationships on a graph. We know that the solution to the system is the point of intersection of two lines.
Keeping all of this in mind, we want to determine if all of us will ever have the same amount of money in our savings accounts. Let's take a look at the system of equations we created in Part A.
y=10x+50 & (I) y=10x+25 & (II)
Using the information that we just reviewed, we can immediately see that this system will not have a solution. The equations have the same slope but different y-intercepts. We can verify this conclusion by graphing both equations on a coordinate plane and looking for a point of intersection.
This means that we will never have the same amount of money in our savings account as our friend has in theirs.
