Questions: Solve by the elimination method. 6x + 4y = -16 -6x + y = 41 Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. The solution is (Simplify your answer. Type an ordered pair.) B. There are infinitely many solutions. C. There is no solution.

Solution Steps

To solve the system of equations using the elimination method, we aim to eliminate one of the variables by adding or subtracting the equations. Here, we can add the two equations to eliminate \(x\) because the coefficients of \(x\) are opposites. After eliminating \(x\), we solve for \(y\) and then substitute back to find \(x\).

We start with the following system of equations: \[ \begin{align*}

1. & \quad 6x + 4y = -16 \\
2. & \quad -6x + y = 41 \end{align*} \]

To eliminate \(x\), we can add both equations: \[ (6x + 4y) + (-6x + y) = -16 + 41 \] This simplifies to: \[ 5y = 25 \]

Dividing both sides by 5 gives: \[ y = 5 \]

Now, we substitute \(y = 5\) back into one of the original equations. Using the second equation: \[ -6x + 5 = 41 \] Rearranging gives: \[ -6x = 36 \quad \Rightarrow \quad x = -6 \]

Final Answer