Use Cramer's rule to find the number of items the company must sell each week to break even.

y= 20x + 200
y= 25x
D= |20 -1|. -20 - (-25)
. |25 -1| D= 5

Dx= |200 -1|. -200 - 0
. |0 -1| Dx= -200

Dy= |20 200|. 0 - 5000
. |25 0 | Dy= -5000

x= Dx/D x= -200/5 x= -40
y= Dy/D y= -5000/5 y= -1000

Is This Right?

20 x - 1 y = -200

25 x - 1 y = 0

D = -20 + 25 = 5

Dx =
| -200 -1 |
| +000 -1 | / 5

= 200/5 = 40 sign ?

Dy =
| 20 -200 |
| 25 +000 | /5

= 5000/5 = 1000

Yes, your calculations using Cramer's rule are correct. To find the number of items the company must sell each week to break even, you need to solve the system of equations:

y = 20x + 200
y = 25x

Using Cramer's rule, you need to calculate the determinant (D), the determinant of x (Dx), and the determinant of y (Dy).

The determinant (D) is calculated by taking the determinant of the coefficients of x and y in the system of equations:

D = |20 -1|
|25 0 |

Calculating the determinant, we get D = (20*0) - (25*-1) = -5.

The determinant of x (Dx) is calculated by replacing the coefficients of x with the constant terms in the system of equations:

Dx = |200 -1|
| 0 -1|

Calculating the determinant, we get Dx = (200*-1) - (0*-1) = -200.

Similarly, the determinant of y (Dy) is calculated by replacing the coefficients of y with the constant terms:

Dy = |20 200|
|25 0|

Calculating the determinant, we get Dy = (20*0) - (25*200) = -5000.

Finally, the value of x can be found by dividing Dx by D:

x = Dx / D = -200 / -5 = 40.

Similarly, the value of y can be found by dividing Dy by D:

y = Dy / D = -5000 / -5 = 1000.

Therefore, the company needs to sell 40 items each week to break even.