Sure, let's solve the given system of equations step by step.
### Step 1: Solve for [tex]\( \square \)[/tex]
We start with the first equation:
[tex]\[ \square - 9 = 19 \][/tex]
To isolate [tex]\( \square \)[/tex], we add 9 to both sides of the equation:
[tex]\[ \square = 19 + 9 \][/tex]
[tex]\[ \square = 28 \][/tex]
### Step 2: Solve for [tex]\( \theta \)[/tex]
Next, we use the second equation:
[tex]\[ \square + \theta = 28 \][/tex]
We know that [tex]\( \square = 28 \)[/tex] (from Step 1), so we can substitute this value into the equation:
[tex]\[ 28 + \theta = 28 \][/tex]
To solve for [tex]\( \theta \)[/tex], we subtract 28 from both sides:
[tex]\[ \theta = 28 - 28 \][/tex]
[tex]\[ \theta = 0 \][/tex]
### Step 3: Verify the third equation
The third equation seems a bit unclear, but let's analyze it based on the interpretation that we need to add some given values:
[tex]\[ \square + \theta = ? \][/tex]
[tex]\[ \square + \theta = 16 \][/tex]
We know [tex]\( \square = 28 \)[/tex] and [tex]\( \theta = 0 \)[/tex] (from previous steps):
[tex]\[ 28 + 0 = 28 \][/tex]
So the correct interpretation of the equation is:
[tex]\[ 28 = 16 \][/tex]
### Step 4: Summary
Let’s summarize our findings:
- [tex]\( \square = 28 \)[/tex]
- [tex]\( \theta = 0 \)[/tex]
- The result of [tex]\( \square + \theta \)[/tex] is [tex]\( 28 \)[/tex]
- The given addition value was [tex]\( 16 \)[/tex], which doesn't match our derived value of [tex]\( 28 \)[/tex].
Thus we have the values:
[tex]\[ \square = 28, \theta = 0, \text{ addition 16}, \text{ result } 28 \][/tex]
The step-by-step results are:
1. [tex]\( \square = 28 \)[/tex]
2. [tex]\( \theta = 0 \)[/tex]
3. [tex]\( \square + \theta = 28 \)[/tex]
4. The addition constant [tex]\( = 16 \)[/tex]
5. Verification of [tex]\( \square + \theta \)[/tex] is [tex]\( 28 \)[/tex]
