Taking into account the definition of a system of linear equations, after 4 weeks Juan and Mila will have saved the same amount of money, $120.
A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.
The graphic method consists of representing the graphs associated with the equations of the system to deduce its solution. The solution of the system is the point of intersection between the graphs. The reason for this is that the coordinates of said point satisfy both equations.
In this case, you know:
- At the beginning of the year, Juan had $60 in savings and saved an additional $15 each week thereafter.
- Mila started the year with $40 and saved $20 every week.
So the system of equations is:
J= 60 + 15t
M= 40 + 20t
Graphing both equations (graph attached), you obtain that the solution is the point (4,120). This means that after 4 weeks Juan and Mila will have saved the same amount of money, $120.