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The equations in this sytem were added to solve for x. What is the value of x?

Negative 8 x + 8 y = 8. 3 x minus 8 y = negative 18. Negative 5 x = negative 10.
x = negative 2
x = negative one-half
x = one-half
x = 2

1 answer

To solve the system of equations for \( x \), let's start by simplifying and solving each equation.

We have the following equations:

  1. \(-8x + 8y = 8\)
  2. \(3x - 8y = -18\)
  3. \(-5x = -10\)

Let's solve the third equation first:

\[ -5x = -10 \implies x = \frac{-10}{-5} = 2. \]

So, we've found that \( x = 2 \).

Now, let's verify this value by substituting \( x = 2 \) back into the first two equations to see if it holds.

  1. Substitute \( x = 2 \) into \(-8x + 8y = 8\): \[ -8(2) + 8y = 8 \implies -16 + 8y = 8 \implies 8y = 24 \implies y = 3. \]

  2. Now substitute \( x = 2 \) and \( y = 3 \) into \( 3x - 8y = -18\): \[ 3(2) - 8(3) = 6 - 24 = -18. \]

Both equations hold true when \( x = 2 \) and \( y = 3 \).

Thus, the value of \( x \) is \(\boxed{2}\).