Question

use cramers rule to solve the system or to determine that the system is inconsistent or contains dependent equations.
$5x - 2y = 10$
$4x + 3y = 31$
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set is {}. (simplify your answer. type an ordered pair.)
b. there are infinitely many solutions.
c. there is no solution.

Explanation:

Step1: Calculate coefficient determinant $D$

$$ D =
LATEXBLOCK0
= (5)(3) - (-2)(4) = 15 + 8 = 23 $$

Step2: Calculate $D_x$ (replace x-column)

$$ D_x =
LATEXBLOCK1
= (10)(3) - (-2)(31) = 30 + 62 = 92 $$

Step3: Calculate $D_y$ (replace y-column)

$$ D_y =
LATEXBLOCK2
= (5)(31) - (10)(4) = 155 - 40 = 115 $$

Step4: Solve for $x$ and $y$

$x = \frac{D_x}{D} = \frac{92}{23} = 4$
$y = \frac{D_y}{D} = \frac{115}{23} = 5$

Answer:

A. The solution set is $\{(4,5)\}$.