Floyd Christensen
09/25/2023 · Senior High School
b) \( \begin{array}{ll}x=3 & x-y=1 \\ x=5 & x+y=7\end{array} \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To solve the system of equations given in the form of pairs, we can analyze each pair separately.
1. **First Pair:**
\[
\begin{cases}
x = 3 \\
x - y = 1
\end{cases}
\]
From the first equation, we have \( x = 3 \). We can substitute this value into the second equation:
\[
3 - y = 1
\]
Solving for \( y \):
\[
-y = 1 - 3 \\
-y = -2 \\
y = 2
\]
So, the solution for the first pair is \( (x, y) = (3, 2) \).
2. **Second Pair:**
\[
\begin{cases}
x = 5 \\
x + y = 7
\end{cases}
\]
From the first equation, we have \( x = 5 \). We can substitute this value into the second equation:
\[
5 + y = 7
\]
Solving for \( y \):
\[
y = 7 - 5 \\
y = 2
\]
So, the solution for the second pair is \( (x, y) = (5, 2) \).
In summary, the solutions for the pairs of equations are:
- For the first pair: \( (3, 2) \)
- For the second pair: \( (5, 2) \)
Quick Answer
For the first pair: \( (3, 2) \)
For the second pair: \( (5, 2) \)
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