Pregunta
esystem \( y=4 x-3 \) and \( y=4 x+3 \)
Ask by Osborne Ramirez. in the United States
Jan 23,2025
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The system has no solution.
Solución
Solve the system of equations \( y=4x-3;y=4x+3 \).
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
\(\left\{ \begin{array}{l}y=4x-3\\y=4x+3\end{array}\right.\)
- step1: Substitute the value of \(y:\)
\(4x-3=4x+3\)
- step2: Cancel equal terms:
\(-3=3\)
- step3: The statement is false:
\(x \in \varnothing \)
- step4: Calculate:
\(\left\{ \begin{array}{l}x \in \varnothing \\y \in \varnothing \end{array}\right.\)
- step5: Rewrite:
\((x, y) \in \varnothing\)
The system of equations \(y=4x-3\) and \(y=4x+3\) has no solution. This means that there is no point that satisfies both equations simultaneously.
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Bonus Knowledge
Did you know that the equations \( y=4x-3 \) and \( y=4x+3 \) represent two parallel lines? Since they have the same slope (which is 4), they will never intersect on a graph, creating a pair of lines that will always maintain the same distance from each other! To visualize this in real life, think of the routing paths for two cars on a busy road; they may be traveling alongside each other, maintaining a steady gap without crossing paths. You can sketch these lines on a graph, and you'll see just how parallelism works in coordinate geometry!
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