To determine the number of solutions for the given system of equations:
[tex]\[
\begin{array}{l}
y = 2x + 4 \\
y + 6 = 2x
\end{array}
\][/tex]
we will analyze each equation and then compare them.
1. Rewrite the second equation to match the first equation's format:
[tex]\[
y + 6 = 2x
\][/tex]
Isolate [tex]\(y\)[/tex] on the left side by subtracting 6 from both sides:
[tex]\[
y = 2x - 6
\][/tex]
Now, we have the following system of equations from both transformations:
[tex]\[
\begin{array}{l}
y = 2x + 4 \\
y = 2x - 6
\end{array}
\][/tex]
2. Compare the two equations to find the number of intersections (solutions):
[tex]\[
2x + 4 = 2x - 6
\][/tex]
Subtract [tex]\(2x\)[/tex] from both sides to isolate the constants:
[tex]\[
4 = -6
\][/tex]
Given that [tex]\(4\)[/tex] does not equal [tex]\(-6\)[/tex], this equation has no solution. Thus, there is no [tex]\(x\)[/tex] that satisfies both equations simultaneously.
Therefore, since there is no point [tex]\((x, y)\)[/tex] that satisfies both equations, the system of equations has no solution.
A. No solution is the correct answer.
