Question

solve the system of equations by the addition method.\

$$\begin{cases}4x + y = -2\\\\-12x - 3y = 6\\end{cases}$$

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

Explanation:

Step1: Multiply first equation

Multiply the first equation \(4x + y = -2\) by 3 to make coefficients of \(y\) opposite.
\(3\times(4x + y) = 3\times(-2)\)
\(12x + 3y = -6\)

Step2: Add two equations

Add the new equation \(12x + 3y = -6\) and the second equation \(-12x - 3y = 6\).
\((12x - 12x) + (3y - 3y) = -6 + 6\)
\(0 = 0\)

Answer:

B. There are infinitely many solutions.