Question

type the correct answer in each box. use numerals instead of words. what is the solution to this matrix equation? \\(\

$$\begin{bmatrix}-1 & 4 \\\\ 3 & -2\\end{bmatrix}$$

\

$$\begin{bmatrix}x \\\\ y\\end{bmatrix}$$

=\

$$\begin{bmatrix}-26 \\\\ 8\\end{bmatrix}$$

\\) \\(x = \boxed{}\\) \\(y = \boxed{}\\)

Explanation:

Step1: Convert to linear system

$$\begin{cases} -1x + 4y = -26 \\ 3x - 2y = 8 \end{cases}$$

Step2: Eliminate $y$ (scale eq2)

Multiply the second equation by 2:
$$6x - 4y = 16$$

Step3: Add equations to solve $x$

Add to first equation:
$$(-x + 4y) + (6x - 4y) = -26 + 16$$
$$5x = -10$$
$$x = \frac{-10}{5} = -2$$

Step4: Substitute $x$ to find $y$

Plug $x=-2$ into $3x - 2y = 8$:
$$3(-2) - 2y = 8$$
$$-6 - 2y = 8$$
$$-2y = 8 + 6 = 14$$
$$y = \frac{14}{-2} = -7$$

Answer:

$x = -2$
$y = -7$