Question

solve the system of equations by the addition method.\

$$\begin{cases}x - 6y = 14\\\\-x + 3y = -8\\end{cases}$$

\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: Add the two equations

Add the equations \( x - 6y = 14 \) and \( -x + 3y = -8 \) together.
\( (x - 6y) + (-x + 3y) = 14 + (-8) \)
Simplify the left side: \( x - 6y - x + 3y = -3y \)
Simplify the right side: \( 14 - 8 = 6 \)
So we get \( -3y = 6 \)

Step2: Solve for y

Divide both sides of \( -3y = 6 \) by -3.
\( y = \frac{6}{-3} = -2 \)

Step3: Substitute y into one of the original equations

Substitute \( y = -2 \) into the first equation \( x - 6y = 14 \).
\( x - 6(-2) = 14 \)
Simplify: \( x + 12 = 14 \)
Subtract 12 from both sides: \( x = 14 - 12 = 2 \)

Answer:

A. The solution is \( (2, -2) \)