Question

y = –A system of equations. y equals negative StartFraction one-half EndFraction x plus 4. x plus 2 y equals negative 8.x + 4
x + 2y = –8
How many solutions does this linear system have?

one solution: (8, 0)
one solution: (0, 8)
no solution
infinite number of solutions

Answer 1

To determine the number of solutions for the system of equations given, we first need to rewrite the equations clearly based on the information provided.

1. The first equation appears to be:
\[
y = -\frac{1}{2}x + 4
\]

2. The second equation can be rewritten as:
\[
x + 2y = -8
\]

Now, we can solve this system to see how many solutions it has.

### Step 1: Substitute \( y \) from the first equation into the second equation

Substituting \( y \) from the first equation into the second equation:

\[
x + 2\left(-\frac{1}{2}x + 4\right) = -8
\]

### Step 2: Simplify the equation

Distributing \( 2 \) in the second equation gives:

\[
x - x + 8 = -8
\]

This simplifies to:

\[
8 = -8
\]

### Step 3: Analyze the result

The equation \( 8 = -8 \) is a contradiction, which tells us that the system of equations does not have any solutions.

### Conclusion

The answer is **no solution**.