Question

use cramers rule to solve the system or to determine that the system is inconsistent or contains dependent equations.$2x + y = 9$$3x - 3y = -9$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: Find coefficient determinant $D$

Calculate determinant of coefficient matrix:

$$ D =
LATEXBLOCK0
= (2)(-3) - (1)(3) = -6 - 3 = -9 $$

Step2: Find determinant $D_x$

Replace $x$-column with constants:

$$ D_x =
LATEXBLOCK1
= (9)(-3) - (1)(-9) = -27 + 9 = -18 $$

Step3: Find determinant $D_y$

Replace $y$-column with constants:

$$ D_y =
LATEXBLOCK2
= (2)(-9) - (9)(3) = -18 - 27 = -45 $$

Step4: Calculate $x$ and $y$

Use $x=\frac{D_x}{D}$, $y=\frac{D_y}{D}$:
$x = \frac{-18}{-9} = 2$
$y = \frac{-45}{-9} = 5$

Answer:

A. The solution set is $\{(2, 5)\}$. (Simplify your answer. Type an ordered pair.)