Answer:
To solve the system of equations x + y + 3 = 0 and 2x + 3y - 4 = 0 graphically, we can plot the two lines and find their point of intersection.
First, let's rearrange the equations to the slope-intercept form y = mx + b:
x + y + 3 = 0 => y = -x - 3
2x + 3y - 4 = 0 => y = (-2/3)x + 4/3
Now we can plot these two lines on a graph:
|
3 | o
| /
2 | /
| /
1 | /
| /
0 |/
------------
0 1 2 3
The first line has a y-intercept of -3 and a slope of -1, so we plot a point at (0, -3) and then go down one unit and right one unit to plot another point. We can then draw a line through these two points.
The second line has a y-intercept of 4/3 and a slope of -2/3, so we plot a point at (0,4/3) and then go down two units and right three units to plot another point. We can then draw a line through these two points.
The point where the two lines intersect is the solution to the system. From the graph, we can see that the intersection point is approximately (-3,0).
Therefore, the solution to the system is x = -3 and y = 0.