A system of equations is graphed on the coordinate plane. A student concludes that the solution of the system is $$ (-0.5,1.5) $$. Is this correct? Justify your response.

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To determine whether the point $$(-0.5, 1.5)$$ is the correct solution to the system of equations represented on the coordinate plane, you should follow these steps:

1. **Identify the Equations:**
   - First, ensure you have the exact equations of the system. A system typically consists of two (or more) equations that you solve simultaneously.

2. **Substitute the Point into Each Equation:**
   - Take the $$x$$-coordinate and $$y$$-coordinate of the point and substitute them into both equations.
   - For example, if your system is:
     $$
     \begin{cases}
     y = 2x + 1 \
     y = -x + 2
     \end{cases}
     $$
     Substitute $$x = -0.5$$ and $$y = 1.5$$ into each equation:
     - **First Equation:** $$1.5 = 2(-0.5) + 1 \Rightarrow 1.5 = -1 + 1 \Rightarrow 1.5 = 0$$ (False)
     - **Second Equation:** $$1.5 = -(-0.5) + 2 \Rightarrow 1.5 = 0.5 + 2 \Rightarrow 1.5 = 2.5$$ (False)

3. **Check for Consistency:**
   - If the substituted values satisfy **both** equations, then $$(-0.5, 1.5)$$ is indeed the solution to the system.
   - If the point does **not** satisfy even one of the equations, it is **not** the correct solution.

4. **Graphical Verification (Optional):**
   - Plot both equations on the coordinate plane.
   - The solution to the system is the point where the two lines intersect.
   - Visually verify if $$(-0.5, 1.5)$$ lies at the intersection.

**Conclusion:**

Without the specific equations or the graph, it's impossible to definitively say whether $$(-0.5, 1.5)$$ is the correct solution. However, by following the substitution method outlined above, you can verify the validity of the solution yourself. If after substitution the point satisfies both equations, then the student's answer is correct. Otherwise, it is incorrect.
To check if $$(-0.5, 1.5)$$ is the correct solution, substitute $$x = -0.5$$ and $$y = 1.5$$ into both equations. If the point satisfies both, it's correct; otherwise, it's not.

A system of equations is graphed on the coordinate plane. A student concludes that the solution of the system is \( (-0.5,1.5) \). Is this correct? Justify your response.

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