Question

Which equation results from adding the equations in this system?

Negative 8 x + 8 y = 8. 3 x minus 8 y = negative 18.
5 x = negative 10
5 x = 26
Negative 5 x = 26
Negative 5 x = negative 10

Answer 1

To add the given equations in the system, we first rewrite them clearly:

1. \(-8x + 8y = 8\) (Equation 1)
2. \(3x - 8y = -18\) (Equation 2)

Next, we will add these two equations together.

Starting with Equation 1:
\[
-8x + 8y = 8
\]

And Equation 2:
\[
3x - 8y = -18
\]

Now, we add them line-by-line:

For the \(x\) terms:
\[
-8x + 3x = -5x
\]

For the \(y\) terms:
\[
8y - 8y = 0y \quad (\text{which is just } 0)
\]

For the constant terms:
\[
8 + (-18) = 8 - 18 = -10
\]

Putting it all together, the result of adding the two equations is:
\[
-5x + 0y = -10
\]
or simply:
\[
-5x = -10
\]

Thus, among the options given, the correct equation that results from adding the two equations in the system is:
\[
\text{Negative 5 x = negative 10} \quad \text{(which is -5x = -10)}
\]