Question

Use cramers rule to compute the solutions of the systems
A) -5x₁+2x₂ = 9
3x₁-x₂ = -4

Answer 1

The solution to the system of equations using Cramer's Rule is x₁ = 1 and x₂ = 7.

Step-by-step explanation:

To solve the system of equations using Cramer's Rule, we first find the determinant of the coefficient matrix and the determinants of the matrices formed by replacing one column of the coefficient matrix by the constants from the right-hand side of the equations.

Step 1: Find the coefficient matrix determinant

The coefficient matrix is:

|-5 2|

| 3 -1|

We find its determinant (denoted as D):

D = (-5)(-1) - (2)(3) = 5 - 6 = -1

Step 2: Find the determinant for x₁ (Dx₁)

The matrix for x₁ replaces the first column with the constants:

|-4 -1|

Now find its determinant:

Dx₁ = (9)(-1) - (2)(-4) = -9 + 8 = -1

Step 3: Find the determinant for x₂ (Dx₂)

| 3 -4|

Now find its determinant:

Dx₂ = (-5)(-4) - (9)(3) = 20 - 27 = -7

x₂ = Dx₂ / D = -7 / -1 = 7

x₁ = 1 and x₂ = 7 are the solutions to the system.