Question

use cramers rule to solve the system or to determine that the system is inconsistent or contains dependent equations.$x + y = 8$$x - y = 4$find the determinants.$d = -2$, $d_x = -12$, $d_y = -4$select the correct choice below and, if necessary, fill in the answer box within your choice.$\boldsymbol{\bigcirc}$ a. the solution set is {___}.(type an ordered pair. simplify your answers.)$\boldsymbol{\bigcirc}$ b. the system contains dependent equations.$\boldsymbol{\bigcirc}$ c. the system is inconsistent.

Explanation:

Step1: Calculate x via Cramer's Rule

$x = \frac{D_x}{D} = \frac{-12}{-2} = 6$

Step2: Calculate y via Cramer's Rule

$y = \frac{D_y}{D} = \frac{-4}{-2} = 2$

Step3: Verify system consistency

Since $D
eq 0$, the system has a unique solution, so it is consistent and independent.

Answer:

A. The solution set is $\{(6, 2)\}$