Question
is 5, -1 a solution to the system of these linear equations: x + y = 4 and 2x + 3y = 7? why?
Answers
GPT-4o mini
To determine if the point \( (5, -1) \) is a solution to the system of equations given by:
1. \( x + y = 4 \)
2. \( 2x + 3y = 7 \)
we can substitute \( x = 5 \) and \( y = -1 \) into both equations and check if they hold true.
**For the first equation:**
\[
x + y = 4 \\
5 + (-1) = 4 \\
5 - 1 = 4 \\
4 = 4 \quad \text{(True)}
\]
**For the second equation:**
\[
2x + 3y = 7 \\
2(5) + 3(-1) = 7 \\
10 - 3 = 7 \\
7 = 7 \quad \text{(True)}
\]
Since both equations are satisfied by the point \( (5, -1) \), we conclude that \( (5, -1) \) is indeed a solution to the system of equations.
1. \( x + y = 4 \)
2. \( 2x + 3y = 7 \)
we can substitute \( x = 5 \) and \( y = -1 \) into both equations and check if they hold true.
**For the first equation:**
\[
x + y = 4 \\
5 + (-1) = 4 \\
5 - 1 = 4 \\
4 = 4 \quad \text{(True)}
\]
**For the second equation:**
\[
2x + 3y = 7 \\
2(5) + 3(-1) = 7 \\
10 - 3 = 7 \\
7 = 7 \quad \text{(True)}
\]
Since both equations are satisfied by the point \( (5, -1) \), we conclude that \( (5, -1) \) is indeed a solution to the system of equations.