Certainly! Let's solve the system of linear equations step by step.
We are given the system of equations:
1. [tex]\( x + 2y = 16 \)[/tex]
2. [tex]\( x + 2y = -2 \)[/tex]
### Step 1: Set Up the Equations
Rewrite the two equations for clarity:
[tex]\[
x + 2y = 16 \tag{1}
\][/tex]
[tex]\[
x + 2y = -2 \tag{2}
\][/tex]
### Step 2: Analyze the System
Notice that both equations have the same left-hand side but different right-hand sides. This is a key observation.
### Step 3: Subtract the Equations
To see if there's a common solution, subtract equation (2) from equation (1):
[tex]\[
(x + 2y) - (x + 2y) = 16 - (-2)
\][/tex]
Simplifying the left-hand side, we get:
[tex]\[
0 = 16 + 2
\][/tex]
[tex]\[
0 = 18
\][/tex]
### Step 4: Understand the Implications
The result [tex]\(0 = 18\)[/tex] is a contradiction—it is impossible for zero to equal 18. This implies there is no solution that satisfies both equations simultaneously.
### Conclusion
The system of equations is inconsistent. Thus, there are no values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] that satisfy both equations together.
[tex]\[
\boxed{\text{No Solution}}
\][/tex]
This means the system has no point of intersection, and thus, the solution set is empty:
[tex]\[
\boxed{\emptyset}
\][/tex]
