Question

Algebra Name: ________________________

Systems 4.1 Solving Systems by Graphing (in context) – Practice Learning Targets: I can solve a system of equations in context by graphing. I can interpret the solution of a system of equations. 1. Allison has $200 in her savings account and is saving $20 per week. Her friend Shannon has $500 in
her bank account and is spending $40 per week. When will they have the same amount in their savings accounts?
a. Write TWO equations to represent how many fish each fisherman catches.
Allison:
Shannon:
b. Graph each equation on the same coordinate plane.
(Allison in Green, Shannon in Purple)
c. How many weeks will both friends have the same amount of money? How do you know?
d. How much money will they each have?
e. When will Allison have more money than Shannon? How do you know?

Answer 1

a. Allison is saving $20 per week, starting with $200:

• A = 200 + 20W

Shannon is spending $40 per week, starting with $500:

• S = 500 - 40W

b. graph is attached

c. The both friends will have the same amount of money in 5 weeks

d. Each will have $ 300

e. Allison will have more money after 5 weeks.

How to write the equations

a. The equations to represent how much money each person has.

A = Allison

S = Shannon

W = number of weeks.

Allison is saving $20 per week, starting with $200:

A = 200 + 20W

Shannon is spending $40 per week, starting with $500:

S = 500 - 40W

b. graph is attached

c. The point of intersection on the graph represents the week when both friends will have the same amount of money. (5, 300)

= 5 weeks

d. Each will have $ 300

e. Allison will have more money after the point of intersection of the two graphs. This is from 6 weeks.

Studying the graph, shows that Allison's graph is going up from left to right and increases after the point of intersection. While Shannon's graph became lesser