Bot GPT 4-o mini To solve the system of equations
- \( 5x + y = -3 \)
- \( -5x - y = 3 \)
we can use the method of substitution or elimination. Here, we'll use the elimination method.
First, let's add both equations together:
\[ (5x + y) + (-5x - y) = -3 + 3 \]
This simplifies to:
\[ 0 = 0 \]
Since we get a true statement (0 = 0), it indicates that the two equations represent the same line. Therefore, the system has infinitely many solutions.
To express the solution, we can solve for \( y \) in terms of \( x \) using the first equation:
\[ y = -3 - 5x \]
Thus, the solution can be expressed as:
\[ { (x, -3 - 5x) ; | ; x \in \mathbb{R} } \]
This means that for any real number \( x \), there is a corresponding \( y \) value that satisfies both equations.
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