Kate bought 3 used cds and 1 used dvd at the bookstore. her friend joel bought 2 used cds and 2 used dvds at the same store. if kate spent $20 and joel spent $22, determine the cost of a used cd and a used dvd?

Cost of 1 DVD is $6.5

Cost of one CD is $4.5

Combine cost of one DVD and CD is $11

Step-by-step explanation:

Given :

Kate bought 3 used CDs and 1 used DVD at the bookstore.

Her friend Joel bought 2 used CDs and 2 used DVDs at the same store.

Kate spent $20

Joel spent $22

To Find :  the cost of a used CD and a used DVD

Solution :

Let cost of 1 used CDs be $x

Let cost of 1 used DVDs be $y

Cost of 3 used CDs = $3x

Cost of 2 used CDs = $2x

Cost of 2 used DVDs = $2y

Kate bought 3 used CDs and 1 used DVD at the bookstore.

She spent $20

So, equation becomes :

⇒ ---(a)

Joel bought 2 used CDs and 2 used DVDs. she spent $22.

So, equation becomes:

⇒ --(b)

Now solve (a) and (b) to determine the value of x and y

We will use substitution method

Substitute the value of x from (b) in (a)

Thus cost of 1 DVD is $6.5

Now substitute this value of y in b to get value of x

⇒

⇒

⇒

⇒

⇒

⇒

Thus the cost of one CD is $4.5

Hence the combine cost of one DVD and CD =  $6.5+ $4.5=$11

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!

she was supposed to add the hours(38.5) and multiply the amount of money she earned(7.50) resulting in $288.75 .

correct me if i'm wrong and if it is i'm truly sorry.