To determine how many solutions the given system of equations has, let's analyze and simplify the equations step by step.
The system of equations is:
[tex]\[
\begin{array}{c}
y = -x - 3 \\
2y + 2x = -6
\end{array}
\][/tex]
First, let's simplify the second equation, [tex]\(2y + 2x = -6\)[/tex]:
1. Divide the entire equation by 2 to make it simpler:
[tex]\[
\frac{2y + 2x}{2} = \frac{-6}{2}
\][/tex]
[tex]\[
y + x = -3
\][/tex]
So the second equation simplifies to:
[tex]\[
y + x = -3
\][/tex]
Now let's compare the simplified second equation with the first equation.
The first equation is:
[tex]\[
y = -x - 3
\][/tex]
Rewriting the first equation, we have:
[tex]\[
y + x = -3
\][/tex]
We see that the simplified second equation and the first equation are exactly the same:
[tex]\[
y + x = -3
\][/tex]
Since both equations represent the same line, they do not intersect in just one point or diverge; rather, they overlap completely.
This means the system of equations is dependent and represents the same line.
Therefore, the system has infinitely many solutions, which corresponds to more than 1 solution.
So, the answer is:
[tex]\[ \text{B. More than 1 solution} \][/tex]
