Answer:
Each pencil costs $0.07 and each eraser costs $0.03
Step-by-step explanation:
System of linear equations
It refers to the study of systems when n variables are related in m linear equations, each one is not independent from the others. Solving such systems can be done following very diverse approaches.
Let p=the price of each pencil while e is the price each eraser
Julio bought 4 pencils and 3 erasers, spending
[tex]4p+3e=0.37[/tex]
David bought 3 pencils and 4 erasers, spending
[tex]3p+4e=0.33[/tex]
The system of equations is written in the form
[tex]\left\{\begin{matrix}4p+3e=0.37\\ 3p+4e=0.33\end{matrix}\right[/tex]
We'll solve it by reduction. Multiplying the first equation by -3 and the second by 4:
[tex]\left\{\begin{matrix}-12p-9e=-1.11\\ 12p+16e=1.32\end{matrix}\right.[/tex]
Adding both equations:
7e=0.21
e=0.03
Multiplying the first one by -4 and the second by 3
[tex]\left\{\begin{matrix}-16p-12e=-1.48\\ 9p+12e=0.99\end{matrix}\right.\end{matrix}\right.[/tex]
Adding both equations:
-7p=-0.49
p=0.07
Solution: Each pencil costs $0.07 and each eraser costs $0.03
