Question

solve by graphing

x=2
x+y=-2

Answer 1

To solve the system of equations by graphing, we will graph the two equations:

1. \( x = 2 \)
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:

- When \( x = 0 \):
\[
y = -0 - 2 = -2 \quad \text{(Point: (0, -2))}
\]

- 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

1. Draw the vertical line for \( x = 2 \).
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.