Question

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

Answer 1

To solve for \( x \) in the system of equations given, let's first clearly write the equations and solve them step-by-step.

The provided equations are:
1. \( -2x + y = 8 \) (Equation 1)
2. \( 5x - y = -5 \) (Equation 2)
3. \( 3x = 3 \) (Equation 3)

We can start solving from Equation 3:

\[
3x = 3
\]

Dividing both sides by 3 gives:

\[
x = 1
\]

Now, let's ensure \( x = 1 \) satisfies the other two equations.

**Substituting \( x = 1 \) into Equation 1:**

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

This simplifies to:

\[
-2 + y = 8 \implies y = 8 + 2 \implies y = 10
\]

**Now, substituting \( x = 1 \) into Equation 2**:

\[
5(1) - y = -5
\]

This simplifies to:

\[
5 - y = -5 \implies -y = -5 - 5 \implies -y = -10 \implies y = 10
\]

Both equations give us the same value of \( y \) when substituting \( x = 1\).

Since all equations agree, the value of \( x \) is:

\[
\boxed{1}
\]