Sure, let's solve the system of equations graphically. The system of equations given is:
1. [tex]\( x + y = 0 \)[/tex]
2. [tex]\( x - y + 2 = 0 \)[/tex]
### Step 1: Graph the equations
#### For the first equation [tex]\( x + y = 0 \)[/tex]:
1. Rearrange to the slope-intercept form [tex]\( y = -x \)[/tex].
2. Determine two points that lie on this line:
- When [tex]\( x = 0 \)[/tex], [tex]\( y = 0 \)[/tex], so we have the point [tex]\( (0, 0) \)[/tex].
- When [tex]\( x = 1 \)[/tex], [tex]\( y = -1 \)[/tex], so we have the point [tex]\( (1, -1) \)[/tex].
3. Plot these points on the graph and draw a straight line through them.
#### For the second equation [tex]\( x - y + 2 = 0 \)[/tex]:
1. Rearrange to the slope-intercept form [tex]\( y = x + 2 \)[/tex].
2. Determine two points that lie on this line:
- When [tex]\( x = 0 \)[/tex], [tex]\( y = 2 \)[/tex], so we have the point [tex]\( (0, 2) \)[/tex].
- When [tex]\( x = 1 \)[/tex], [tex]\( y = 3 \)[/tex], so we have the point [tex]\( (1, 3) \)[/tex].
3. Plot these points on the graph and draw a straight line through them.
### Step 2: Identify the intersection point
1. Looking at the graph, find the point where the two lines intersect.
2. The point of intersection represents the solution to the system of equations.
### Step 3: Verify the solution set
By observing the graphs of both equations, the point where the lines intersect is [tex]\( (-1, 1) \)[/tex].
### Solution Set
The solution to the system of equations is [tex]\( x = -1 \)[/tex] and [tex]\( y = 1 \)[/tex]. Therefore, the solution set is:
[tex]\[ \{ (-1, 1) \} \][/tex]
