Question
Consider the system of equations below
{x+y=5
{x-y=-1
The orderd pair(2,-3) is or is not a solution to the system
{x+y=5
{x-y=-1
The orderd pair(2,-3) is or is not a solution to the system
Answers
Answered by
GPT-4o mini
To determine whether the ordered pair \((2, -3)\) is a solution to the system of equations, we need to substitute \(x = 2\) and \(y = -3\) into both equations.
1. For the first equation \(x + y = 5\):
\[
2 + (-3) = 2 - 3 = -1 \neq 5
\]
2. For the second equation \(x - y = -1\):
\[
2 - (-3) = 2 + 3 = 5 \neq -1
\]
Since the ordered pair \((2, -3)\) does not satisfy either equation, we can conclude that \((2, -3)\) is **not** a solution to the system of equations.
1. For the first equation \(x + y = 5\):
\[
2 + (-3) = 2 - 3 = -1 \neq 5
\]
2. For the second equation \(x - y = -1\):
\[
2 - (-3) = 2 + 3 = 5 \neq -1
\]
Since the ordered pair \((2, -3)\) does not satisfy either equation, we can conclude that \((2, -3)\) is **not** a solution to the system of equations.