Question

Use Cramer's rule to solve the system [2x-y=-2, x+2, y=9].
x = ___
y = ___

Answer 1

By applying Cramer's rule to the system of equations, it was determined that x equals 1 and y equals 4.

Step-by-step explanation:

To use Cramer's rule to solve the system (2x - y = -2, x + 2y = 9), we first identify the coefficient matrix, the constant matrix, and then compute the determinants needed.

D = | 2 -1 |
| 1 2 | which equals (2*2 - (-1)*1) = 5.

For x (Dx):
Dx = | -2 -1 |
| 9 2 | which equals (-2*2 - (-1)*9) = 5.

For y (Dy):
Dy = | 2 -2 |
| 1 9 | which equals (2*9 - 1*(-2)) = 20.

So, x = Dx/D = 5/5 = 1 and y = Dy/D = 20/5 = 4.

Therefore, the solution to the system is x = 1 and y = 4.