Question

multiple choice (single sel.. 1 point solution of \\( \

$$\begin{cases} x = 4y \\\\ x + 2y = -12 \\end{cases}$$

\\) is \\(\\_\\_\\_\\_.\\) \\(\mathbf{a}\\) \\( \

$$\begin{cases} x = -4 \\\\ y = -1 \\end{cases}$$

\\) \\(\mathbf{b}\\) \\( \

$$\begin{cases} x = -8 \\\\ y = -2 \\end{cases}$$

\\) \\(\mathbf{c}\\) \\( \

$$\begin{cases} x = 4 \\\\ y = -8 \\end{cases}$$

\\) \\(\mathbf{d}\\) \\( \

$$\begin{cases} x = -4 \\\\ y = 1 \\end{cases}$$

\\))

Explanation:

Step1: Substitute $x=4y$ into 2nd equation

$4y + 2y = -12$

Step2: Combine like terms and solve for $y$

$6y = -12 \implies y = \frac{-12}{6} = -2$

Step3: Substitute $y=-2$ into $x=4y$

$x = 4\times(-2) = -8$

Answer:

B.

$$\begin{cases} x = -8 \\ y = -2 \end{cases}$$