Answer
The system \( x - y = 2 \) and \( x + 2y = -2 \) has an approximate solution of \( (0.7, -1.4) \).
Solution
We start by examining each system of equations to see if it has an approximate solution of \( (0.7, -1.4) \).
### Option 1
The system is
\[
x - y = 2 \quad \text{and} \quad x + 2y = -2.
\]
1. Solve the first equation for \( y \):
\[
y = x - 2.
\]
2. Substitute into the second equation:
\[
x + 2(x - 2) = -2 \quad \Longrightarrow \quad x + 2x - 4 = -2.
\]
3. Combine like terms:
\[
3x - 4 = -2.
\]
4. Solve for \( x \):
\[
3x = 2 \quad \Longrightarrow \quad x = \frac{2}{3} \approx 0.67.
\]
5. Substitute \( x \) back to find \( y \):
\[
y = \frac{2}{3} - 2 = -\frac{4}{3} \approx -1.33.
\]
The approximate solution is \( (0.67, -1.33) \), which is very close to \( (0.7, -1.4) \).
### Option 2
The system is
\[
x - 2y = -2 \quad \text{and} \quad x + y = 2.
\]
1. Solve the second equation for \( x \):
\[
x = 2 - y.
\]
2. Substitute into the first equation:
\[
(2 - y) - 2y = -2 \quad \Longrightarrow \quad 2 - 3y = -2.
\]
3. Solve for \( y \):
\[
-3y = -4 \quad \Longrightarrow \quad y \approx 1.33.
\]
4. Thus, \( x = 2 - 1.33 \approx 0.67 \).
This gives the solution \( (0.67, 1.33) \), which does not match \( (0.7, -1.4) \).
### Option 3
The system is
\[
x - y = 2 \quad \text{and} \quad x - 2y = -2.
\]
1. From the first equation, \( x = y + 2 \).
2. Substitute into the second:
\[
(y + 2) - 2y = -2 \quad \Longrightarrow \quad 2 - y = -2.
\]
3. Solve for \( y \):
\[
-y = -4 \quad \Longrightarrow \quad y = 4.
\]
4. Then, \( x = 4 + 2 = 6 \).
The solution here is \( (6, 4) \), which is not an approximate match.
### Option 4
The system is
\[
x + y = 2 \quad \text{and} \quad x + 2y = -2.
\]
1. Subtract the first equation from the second:
\[
(x + 2y) - (x + y) = -2 - 2 \quad \Longrightarrow \quad y = -4.
\]
2. Substitute \( y = -4 \) into \( x + y = 2 \):
\[
x - 4 = 2 \quad \Longrightarrow \quad x = 6.
\]
This gives the solution \( (6, -4) \), which is not an approximate match.
### Conclusion
Only **Option 1** produces a solution that is approximately \( (0.7, -1.4) \).
\[
\boxed{x - y = 2 \quad \text{and} \quad x + 2y = -2.}
\]
Answered by UpStudy AI and reviewed by a Professional Tutor

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