A + b = 15.6 a + c = 18.3 b + c = 13.9 a + b +c =?

Question

asked Nov 28, 2021 98.2k views

1 Answer

Frederik Gheysels · Answer 1 · 2021-12-03T03:50:11+0000

Answer:

a+b+c=23.9

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:

a,b,c

And we have three equations:

$a+b=15.6\\a+c=18.3\\b+c=13.9$

We can solve this system of linear equations in many ways:

Let's use substitution:

Let:

$a+b=15.6\hspace{10}(1)\\a+c=18.3\hspace{10}(2)\\b+c=13.9\hspace{10}(3)$

For (1)

$b=15.6-a\hspace{10}(4)$

Replace (4) into (3)

$(15.6-a)+c=13.9\\15.6-a+c=13.9\\c=-1.7+a\hspace{10}(5)$

Replace (5) into (2)

$a+(-1.7+a)=18.3\\a-1.7+a=18.3\\2a=20\\a=(20)/(2)\\ a=10\hspace{10}(6)$

We have found a, so it will be much easier from here:

Replace (6) into (4)

$b=15.6-a\\b=15.6-10=5.6\\b=5.6\hspace{10}(7)$

Replace (6) into (5)

$c=-1.7+a\\c=-1.7+10=8.3\\c=8.3\hspace{10}(8)$

Therefore:

$a+b+c\\\\(10)+(5.6)+(8.3)\\\\10+5.6+8.3=23.9$