Answer:
[tex]a+b+c=23.9[/tex]
Step-by-step explanation:
Before proceeding to solve a system of linear equations, we have to answer the following question:
The number of unknowns equals the number of equations? If this is true, then we will be able to solve the problem
As you can see we have three unknowns:
[tex]a,b,c[/tex]
And we have three equations:
[tex]a+b=15.6\\a+c=18.3\\b+c=13.9[/tex]
We can solve this system of linear equations in many ways:
Let's use substitution:
Let:
[tex]a+b=15.6\hspace{10}(1)\\a+c=18.3\hspace{10}(2)\\b+c=13.9\hspace{10}(3)[/tex]
For (1)
[tex]b=15.6-a\hspace{10}(4)[/tex]
Replace (4) into (3)
[tex](15.6-a)+c=13.9\\15.6-a+c=13.9\\c=-1.7+a\hspace{10}(5)[/tex]
Replace (5) into (2)
[tex]a+(-1.7+a)=18.3\\a-1.7+a=18.3\\2a=20\\a=\frac{20}{2}\\ a=10\hspace{10}(6)[/tex]
We have found a, so it will be much easier from here:
Replace (6) into (4)
[tex]b=15.6-a\\b=15.6-10=5.6\\b=5.6\hspace{10}(7)[/tex]
Replace (6) into (5)
[tex]c=-1.7+a\\c=-1.7+10=8.3\\c=8.3\hspace{10}(8)[/tex]
Therefore:
[tex]a+b+c\\\\(10)+(5.6)+(8.3)\\\\10+5.6+8.3=23.9[/tex]
