Elliot has a total of 26 books. he has 12 more fiction books than nonfiction books. let x represent the number of fiction books and y represent the number of nonfiction books.
the system of equations models the total costs for each.
x + y = 26
x – y = 12
elliot added the two equations and the result was
2x = 38.
solve the equation. how many of each type of book does elliot have?

fiction books

nonfiction books

Answers

19 fiction books

7 nonfiction books

Explanation

x + y = 26   (i)

x – y = 12   (ii)

Elliot added the two equations and the result was

2x = 38.

Dividing both sides by 2;

x = 19

There are 19 fiction books.

Substituting x in equation (i),

x + y = 26             when x = 19

19 + y = 26

y = 26 - 19

   = 7

There are 7 nonfiction books

After solving the system of equations, Elliot has 19 fiction books and 7 nonfiction books.

Given the following system of equations:

Adding the two equations together, we have:

Dividing both sides by 2, we have:

x = 19 fiction books.

To find the value of y:

y = 7 nonfiction books.

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step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be