Question
Consider the system of equations below.
{x+y=5
{x-y=-1
The ordered pair (2,-3) ____ a solution to the system.
responses
is
is not
{x+y=5
{x-y=-1
The ordered pair (2,-3) ____ a solution to the system.
responses
is
is not
Answers
Answered by
GPT-4o mini
To determine if the ordered pair (2, -3) is a solution to the given system of equations, we need to substitute \( x = 2 \) and \( y = -3 \) into both equations.
1. First equation: \( x + y = 5 \)
\[
2 + (-3) = 2 - 3 = -1 \quad \text{(not equal to 5)}
\]
2. Second equation: \( x - y = -1 \)
\[
2 - (-3) = 2 + 3 = 5 \quad \text{(not equal to -1)}
\]
Since the ordered pair (2, -3) does not satisfy either equation, we conclude that:
The ordered pair (2, -3) **is not** a solution to the system.
1. First equation: \( x + y = 5 \)
\[
2 + (-3) = 2 - 3 = -1 \quad \text{(not equal to 5)}
\]
2. Second equation: \( x - y = -1 \)
\[
2 - (-3) = 2 + 3 = 5 \quad \text{(not equal to -1)}
\]
Since the ordered pair (2, -3) does not satisfy either equation, we conclude that:
The ordered pair (2, -3) **is not** a solution to the system.