To solve the system of equations by graphing, we will graph the two equations:
- \( x = 2 \)
- \( x + y = -2 \)
Step 1: Graph \( x = 2 \)
This equation represents a vertical line that crosses the x-axis at \( x = 2 \). The line extends infinitely in the positive and negative y-directions but stays vertical at \( x = 2 \).
Step 2: Graph \( x + y = -2 \)
We can rewrite this equation in slope-intercept form (\( y = mx + b \)):
\[ y = -x - 2 \]
Now we can find some points to graph this line:
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When \( x = 0 \): \[ y = -0 - 2 = -2 \quad \text{(Point: (0, -2))} \]
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When \( x = -2 \): \[ y = -(-2) - 2 = 0 \quad \text{(Point: (-2, 0))} \]
-
When \( x = -4 \): \[ y = -(-4) - 2 = 2 \quad \text{(Point: (-4, 2))} \]
Now we have enough points to plot the line:
- Point (0, -2)
- Point (-2, 0)
- Point (-4, 2)
Step 3: Graph the Lines
- Draw the vertical line for \( x = 2 \).
- Draw the line for \( y = -x - 2 \) using the points we found.
Step 4: Find the Intersection
The solution to the system of equations is the point where the two lines intersect.
Intersection Point: To find this point, substitute \( x = 2 \) into the second equation:
\[ 2 + y = -2 \]
Solving for \( y \):
\[ y = -2 - 2 \] \[ y = -4 \]
Conclusion
Thus, the solution to the system of equations is:
\[ \boxed{(2, -4)} \]
This point \( (2, -4) \) is where the lines intersect on the graph, confirming the solution visually and algebraically.