Question

Solve the system of linear equations. Then, state whether the system is independent, dependent, or inconsistent. Match your answer to the correct answerbelow.2x+y=-38x+4y=-15Select one:O a. (2,-2), independentO b. (3,-1), independentOc. ((x,y) ly--3+2x), dependentO d. Inconsistent

Answer 1

Given:

$\begin{gathered} 2x+y=-3..............(1) \\ 8x+4y=-15..............(2) \end{gathered}$

To find:

The solutions

Explanation:

Multiplying the equation (1) by 4, get

$8x+4y=-12..............(3)$

Subtract (3) from (2), we get

$\begin{gathered} \begin{equation*} 8x+4y=-15 \end{equation*} \\ (-)8x+(-)4y=(-)-12 \\ -------- \\ 0=-3 \end{gathered}$

But,

$0\ne-3$

Therefore, the system has no solutions.

That is,

The system is inconsistent.

Final answer: Option d.

Inconsistent.