To write the system of equations shown in the graph, you'll need to identify the two equations that correspond to the lines depicted. Based on the options you've provided, I can help clarify how to choose the correct set of equations.
Here are the options you've provided:
- \( \begin{cases} y = 2x + 1 \ y = 4x - 3 \end{cases} \)
- \( \begin{cases} y = -x + 2 \ y = 3x + 4 \end{cases} \)
- \( \begin{cases} y = 2x - 1 \ y = 4x + 3 \end{cases} \)
- \( \begin{cases} y = 2x - 1 \ y = 4x + 0.75 \end{cases} \)
To select the appropriate system of equations, look for the equations that accurately represent the slopes and intercepts of the lines displayed in the graph. If the graph is available, you can describe its characteristics (like slopes, y-intercepts, etc.) to identify the correct equations.
If I had to make a guess without seeing the graph:
- If one line has a slope of 2 and y-intercept of -1, it could correspond to \(y = 2x - 1\).
- If another line has a slope of 4 and a y-intercept of 3 or 0.75, it could correspond to either \(y = 4x + 3\) or \(y = 4x + 0.75\).
Please verify with the graph to ensure you're choosing the right combination. However, based on common possible intersections and slopes, one of these is typically correct. If you can provide more context or describe the graph, I could give you more precise guidance!