It looks like there might be a small typographical error in the second equation you've provided, as "yx+2" does not represent a standard linear equation. To proceed, I'll assume you intended to write a different linear equation. If you meant to write \( y = -\frac{1}{2}x + 2 \), or any other specific linear equation, please confirm or correct it.
For now, I will graph the first equation and assume a general second one as an example. However, since we need to determine how many solutions there are based on the equations provided, let's analyze the first equation you gave:
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First Equation: \( y = 3x + 5 \)
- This is a line with a slope of 3 and a y-intercept of 5.
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Second Equation: Assuming you meant a commonly structured linear equation, we can take \( y = -\frac{1}{2}x + 2 \) (you can replace it with the correct second equation if this is not what you meant).
- This line has a slope of -\frac{1}{2} and a y-intercept of 2.
Graphing the Equations
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For \( y = 3x + 5 \):
- When \( x = 0 \), \( y = 5 \) (point is (0,5)).
- When \( x = -1 \), \( y = 2 \) (point is (-1,2)).
You can plot these points on a graph and draw the line extending infinitely in both directions.
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For \( y = -\frac{1}{2}x + 2 \):
- When \( x = 0 \), \( y = 2 \) (point is (0,2)).
- When \( x = 2 \), \( y = 1 \) (point is (2,1)).
Again, plot these points and draw the line.
Determining Solutions
- If these two lines intersect at a single point, the system has exactly one solution.
- If the lines are parallel (same slope, different y-intercepts), the system has no solutions.
- If the lines are coincident (the same line), the system has infinitely many solutions.
Conclusion
To provide a definitive answer about the number of solutions, we need the exact formula or description of the second equation. Please clarify or confirm the intended equation, and then we can accurately determine and visualize the solution.
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