Eli read four more biographies than historical fiction book during the semester. he also read two fewer mysteries than historical fiction books. if he read a total of eleven books during the semester how many of each type of books did he read?

Eli read 3 historical fiction books , 7 biographies and 1 mystery book.

Step-by-step explanation:

Let x be the number of historical fiction books Eli read.

Then, Number of biographies he read = x+4

Number of mysteries he read = x-2

If he read a total of eleven books during the semester , then we have the following equation :

 (Subtract 2 from both sides )

 (Divide both sides by 3)

Therefore , Number of historical fiction books Eli read = 3

Number of biographies he read = 3+4=7

Number of mysteries he read =3-2=1

Hence, Eli read 3 historical fiction books , 7 biographies and 1 mystery book.

the number of biographies books that Eli read is 7

the number of historical fiction books that Eli read is 3

the number of mysteries books that Eli read is 1

Step-by-step explanation:

Let x represent the number of biographies books that Eli read.

Let y represent the number of historical fiction books that Eli read.

Let z represent the number of mysteries books that Eli read.

Eli read four more biographies than historical fiction book during the semester. This means that

x = y + 4

He also read two fewer mysteries books than historical fiction books. This means that

z = y - 2

If he read a total of eleven books during the semester, it means that

x + y + z = 11 - - - - - - - - - - - - 1

Substituting x = y + 4 and z = y - 2 into equation 1, it becomes

y + 4 + y + y - 2 = 11

3y + 2 = 11

3y = 11 - 2 = 9

y = 9/3 = 3

z = y - 2 = 3 - 2 = 1

x = y + 4 = 3 + 4 = 7

center= (-2,0)

radius= sqrt2/2

step-by-step explanation:

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3