Answer:
Part a) The graph in the attached figure (see the explanation)
Part b) The friend is not correct
Step-by-step explanation:
The questions are
a. Write and graph a system of linear equations that represent the amounts in each of your savings accounts
b. Your friend says that in 10 weeks you will both have the same amount of money in your savings accounts. Is your friend correct? Use the graph from part (a) to explain your answer.
Part a)
Let
x ----> the number of weeks
y ---> the amount in the saving account
we know that
The linear equation in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope or unit rate of the linear equation
b is the y-intercept or initial value of the linear equation
In this problem we have
Your saving accounts
The slope is equal to [tex]m=\$10\ each\ week[/tex]
The y-intercept is equal to [tex]b=\$90[/tex]
substitute
[tex]y=10x+90[/tex] ----> equation A
Your friend saving accounts
The slope is equal to [tex]m=\$15\ each\ week[/tex]
The y-intercept is equal to [tex]b=\$35[/tex]
substitute
[tex]y=15x+35[/tex] ----> equation B
using a graphing tool
the graph in the attached figure
Part b) Your friend says that in 10 weeks you will both have the same amount of money in your savings accounts. Is your friend correct? Use the graph from part (a) to explain your answer
we know that
When solving a system of equations by graphing, the solution of the system is the intersection point both graphs
In this problem, the intersection point is (11,200)
That means ----> In 11 weeks, both you and your friend have the same amount of money saved up, $200
Therefore
The friend is not correct
