x+y=0

3x+y=-4

Sovle each system of equation by graphing.

If got the answer (-3,3), but it's not there.

Please explain!

by graphing. Plot the following lines

y=-x
y=-3x-4
where they cross is the solution. It is not -3,3

To solve the system of equations by graphing, you will need to plot the lines represented by each equation on a graph and find the point where they intersect. Let's go step by step:

1. Start by rewriting each equation in slope-intercept form (y = mx + b) to make it easier to graph.

For the first equation: x + y = 0, we can isolate y by subtracting x from both sides. So we get: y = -x + 0, which simplifies to y = -x.

For the second equation: 3x + y = -4, isolate y by subtracting 3x from both sides. We have: y = -3x - 4.

2. Now we have the equations in slope-intercept form, so we can easily find two points on each line.

For the first equation, when x = 0, y = 0, giving us the point (0, 0).
When x = 2, y = -2, giving us the point (2, -2).

For the second equation, when x = 0, y = -4, giving us the point (0, -4).
When x = 1, y = -7, giving us the point (1, -7).

3. Plot these points on a graph and draw a straight line through each pair of points for both equations.

The graph should show a downward sloping line passing through the points (0, 0) and (-2, 2) for the first equation (y = -x).

The graph should also show a downward sloping line passing through the points (0, -4) and (1, -7) for the second equation (y = -3x - 4).

4. Finally, find the coordinates of the point where the two lines intersect. This is the solution to the system of equations.

Looking at the graph, you'll notice that the two lines do not intersect at any point. Therefore, there is no solution to this system of equations. This means the system of equations is inconsistent, and there are no values of x and y that satisfy both equations simultaneously.

If you obtained the point (-3, 3) as a potential solution, you might want to double-check your calculations or equation solving methods to ensure accuracy.