Question

question 6 of 10, step 1 of 1 use any convenient method to determine whether the following system of equations is consistent, inconsistent, or dependent. \\(\

$$\begin{cases} 2x - 4y = -12 \\\\ -6x + 12y = 38 \\end{cases}$$

\\) answer \\(\circ\\) only one solution \\(\circ\\) inconsistent system \\(\circ\\) dependent system

Explanation:

Step1: Simplify first equation

Divide $2x - 4y = -12$ by 2:
$\frac{2x}{2} - \frac{4y}{2} = \frac{-12}{2}$
$x - 2y = -6$

Step2: Scale simplified first equation

Multiply by -3 to match x-coefficient:
$-3(x - 2y) = -3(-6)$
$-3x + 6y = 18$

Step3: Compare to second equation

Second equation: $-6x + 12y = 38$, divide by 2:
$\frac{-6x}{2} + \frac{12y}{2} = \frac{38}{2}$
$-3x + 6y = 19$

Step4: Analyze consistency

We have $-3x + 6y = 18$ and $-3x + 6y = 19$, which are contradictory (same left side, different right sides).

Answer:

○ Inconsistent System