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

Negative 2 x + y = 8. 5 x minus y = negative 5. 3 x = 3.
x = negative 3
x = negative 1
x = 1
x = 3

1 answer

To solve for \( x \) in the given system of equations, we should isolate it from the equations provided. The equations you provided are:

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

Let’s start by solving the simplest equation, which is \(3x = 3\):

\[ 3x = 3 \]

Dividing both sides by 3 gives:

\[ x = 1 \]

Now, we can check if this value is consistent with the other equations.

Substituting \( x = 1 \) into the first equation:

\[ -2(1) + y = 8 \] \[ -2 + y = 8 \] \[ y = 8 + 2 = 10 \]

Now substituting \( x = 1 \) and \( y = 10 \) into the second equation:

\[ 5(1) - 10 = -5 \] \[ 5 - 10 = -5 \] \[ -5 = -5 \quad \text{(This is true)} \]

Since both the first and second equations are satisfied with \( x = 1 \) and \( y = 10 \), we conclude that:

\[ \boxed{1} \]

Thus, the value of \( x \) is \( 1 \).