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.

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.
Transcript text: Solve by the elimination method. \[ \begin{array}{l} 6 x+4 y=-16 \\ -6 x+y=41 \end{array} \] Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. The solution is $\square$ (Simplify your answer. Type an ordered pair.) B. There are infinitely many solutions. C. There is no solution.
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Solution

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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 xx because the coefficients of xx are opposites. After eliminating xx, we solve for yy and then substitute back to find xx.

Step 1: Write the System of Equations

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

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

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

Step 3: Solve for yy

Dividing both sides by 5 gives: y=5 y = 5

Step 4: Substitute Back to Find xx

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

Final Answer

The solution to the system of equations is: (6,5) \boxed{(-6, 5)}

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