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Which equation results from adding the equations in this system?

Negative 6 x + 4 y = negative 8. 6 x minus 12 y = 14.
Negative 16 y = 6
Negative 8 y = 6
Negative 8 y = negative 22
Negative 16 y = negative 22

1 answer

To add the given equations in the system:

  1. First equation: \[ -6x + 4y = -8 \]

  2. Second equation: \[ 6x - 12y = 14 \]

Now, let's add the two equations together:

\[ (-6x + 4y) + (6x - 12y) = -8 + 14 \]

Combine like terms:

  • The \(x\) terms: \(-6x + 6x = 0\)
  • The \(y\) terms: \(4y - 12y = -8y\)
  • The constants: \(-8 + 14 = 6\)

So combining all of this, we get:

\[ 0x - 8y = 6 \]

This simplifies to:

\[ -8y = 6 \]

Thus, the correct equation that results from adding the two original equations is:

\[ -8y = 6 \]

So the answer is: Negative 8 y = 6.