Given:
Elliot has a total of 26 books. He has 12 more fiction books than nonfiction books.
To Find:
A system of linear equations represents the situation.
Answer:
[tex]x+y=26\\\\x=y+12[/tex]
Step-by-step explanation:
We are given that x represents the number of fiction books and y is the number of non-fiction books.
We are also given that the total number of books Elliot has is 26 which includes both fiction and non-fiction. So, we may write
[tex]x+y=26[/tex]
Next, we are given that there are 12 more fiction books than non-fiction books. This means, the fiction books are more in number and so, we may write
[tex]x=y+12[/tex]
So, the total system of equations can be represented as
[tex]x+y=26\\\\x=y+12[/tex]
The concept of the linear system is applied.
The two-variable linear system represents the situation. The value of fiction books is 19 and non-fiction books is 7.
It is one dimension figure which has length but no width. A line is made up of an infinite number of points extended side by side.
Given
12 more fiction books than non-fiction.
Elliot has a total of 26 books.
Let x represent the number of fiction books and y represent the number of non-fiction books.
Elliot has a total of 26 books, then
x + y = 26 .....(1)
He has 12 more fiction books than non-fiction books, then
x - y = 12 .....(2)
Form equations 1 and 2,
[tex]\begin{aligned} \rm 2x &= 38\\\rm x &= 19\\\end{aligned}[/tex]
Put the value of x in equation 1
[tex]\begin{aligned} \rm x + y &= 26\\\rm 19 + y &= 26\\\rm y &= 26-19\\\rm y &= 7\\\end{aligned}[/tex]
The value of fiction books is 19 and non-fiction books is 7.
More about the linear system link is given below.
https://brainly.com/question/4695375
