Question

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

Answer 1

`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:

• Substitution Method
• Graphing Method
• Elimination Method

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`