Identify the x-value of the systems of equations: y = x - 8 and 2x + y = 1.

Understand the Problem

The question is asking to identify the x-value for the given system of equations by solving them simultaneously.

Answer

The x-value is $3$.

Steps to Solve

Substituting the first equation into the second

We start with the two equations:

$$ y = x - 8 $$

$$ 2x + y = 1 $$

Substitute $y$ from the first equation into the second equation:

$$ 2x + (x - 8) = 1 $$

Simplifying the equation

Now simplify the equation:

$$ 2x + x - 8 = 1 $$

Combine like terms:

$$ 3x - 8 = 1 $$

Solving for x

Next, add 8 to both sides to isolate the term with $x$:

$$ 3x = 1 + 8 $$

$$ 3x = 9 $$

Now, divide both sides by 3:

$$ x = \frac{9}{3} $$

$$ x = 3 $$

The value of $x$ is $3$.

More Information

This system of equations represents two lines on a graph. The point where they intersect is the solution to the system, which, in this case, is when $x = 3$.

Tips

Forgetting to substitute correctly.
Losing a negative sign during simplification.
Not combining like terms properly.

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