Question

solve the system of equations by the substitution method.\

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

\
select the correct choice below and, if necessary, fill in the answer box to complete your choice.\
\\(\bigcirc\\) a. the solution is \\(\square\\).\
\\(\quad\\) (type an ordered pair. simplify your answer.)\
\\(\bigcirc\\) b. there are infinitely many solutions.\
\\(\bigcirc\\) c. there is no solution.

Explanation:

Step1: Solve the second equation for y

From \(-2x = y + 4\), we can get \(y=-2x - 4\)

Step2: Substitute y into the first equation

Substitute \(y = - 2x-4\) into \(12x + 6y=6\), we have:
\(12x+6(-2x - 4)=6\)

Step3: Simplify and solve for x

Expand the left - hand side: \(12x-12x-24 = 6\)
Combine like terms: \((12x-12x)-24=6\), which simplifies to \(-24 = 6\)
This is a contradiction, which means there is no solution for this system of equations.

Answer:

C. There is no solution.