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.
$d = \square$, $d_x = \square$, $d_y = \square$

Explanation:

Step1: Compute determinant $D$

$$ D =
LATEXBLOCK0
= (1)(-1) - (1)(1) = -1 - 1 = -2 $$

Step2: Compute determinant $D_x$

$$ D_x =
LATEXBLOCK1
= (8)(-1) - (1)(4) = -8 - 4 = -12 $$

Step3: Compute determinant $D_y$

$$ D_y =
LATEXBLOCK2
= (1)(4) - (8)(1) = 4 - 8 = -4 $$

Step4: Solve for $x$ and $y$

$x = \frac{D_x}{D} = \frac{-12}{-2} = 6$, $y = \frac{D_y}{D} = \frac{-4}{-2} = 2$

Answer:

$D=-2$, $D_x=-12$, $D_y=-4$
The solution to the system is $x=6$, $y=2$