Which equation results from adding the equations in this system?

Question

x + 6 y = 9. Negative x + 2 y = negative 15.
8 y = negative 6
8 y = 6
4 y = 24
4 y = negative 6

Answer 1

To find the resulting equation from adding the two equations in the system:

1. The original equations are:

   • Equation 1: \( x + 6y = 9 \)
   • Equation 2: \( -x + 2y = -15 \)

2. Now add both equations together:

\[ (x + 6y) + (-x + 2y) = 9 + (-15) \]

This simplifies to:

\[ x - x + 6y + 2y = 9 - 15 \]

Which further simplifies to:

\[ 0 + 8y = -6 \]

Thus, the resulting equation from adding these two equations is:

\[ 8y = -6 \]

So among the options you've provided, the correct choice is:

8 y = negative 6.