Taking into account the definition of a system of linear equations, Ana bougth:
- 41-cent stamps: 8
- 26-cent stamps: 3
System of linear equations
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.
This case
In this case, a system of linear equations must be proposed taking into account that:
- "x" is the number of 41-cent stamps she bought.
- "y" is the number of 26-cent stamps she bought.
Ana spent $4.06 buying stamps. The number of 41-cent stamps she bought was 5 more than the number of 26-cent stamps. So, the system of equations to be solved is
[tex]\left \{ {{0.41x+0.26y=4.06} \atop {x=y+5}} \right.[/tex]
There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, substituting the second equation in the first you get:
0.41×(y+5)+0.26y=4.06
Solving:
0.41×y+0.41×5+0.26y=4.06
0.41y+2.05+0.26y=4.06
0.41y+0.26y=4.06 - 2.05
0.67y=2.01
y= 2.01÷0.67
y= 3
Remembering that x=y+5, then x=3+5=8
Finally, Ana bougth:
- 41-cent stamps: 8
- 26-cent stamps: 3
Learn more about system of equations:
brainly.com/question/14323743
brainly.com/question/1365672
brainly.com/question/20533585
brainly.com/question/20379472
#SPJ6
