Solve the system by graphing.

x+y=−2
y=13x+2

A. (6, 4); The image is of a 2-dimensional graph with an x-axis and a y-axis. One line is drawn passing through co-ordinates (-3,1) and (3,3). Another line is drawn from co-ordinate (-2,-4) to (6,4).
B. (−3, 1); The image is of a 2-dimensional graph with an x-axis and a y-axis. One line is drawn passing through co-ordinates (-3,1) and (3,3). Another line is drawn from co-ordinate (-4,2) to (2,-4). They intersect each other at (-3,1).
C. (3, 1); The image is of a 2-dimensional graph with an x-axis and a y-axis. One line is drawn passing through co-ordinates (0,2) and (3,1). Another line is drawn from co-ordinate (-2,-4) to (6,4). They intersect each other at (3,1).
D. (0, −2); The image is of a 2-dimensional graph with an x-axis and a y-axis. One line is drawn passing through co-ordinates (0,-2) and (3,-1). Another line is drawn from co-ordinate (-2,-4) to (5,3). They intersect each other at (0,-2).

so, did you graph it?

Which choice matches your findings?

I don't know how to read a grapg but I graphed it. If I know the ordered pair I can use that to see if my graph is sorta correct.

I don't understand the words I can understand a graph which I can clearly see. A graph in words is so confusing.

You have the equations

x+y=−2
y=13x+2

You know it is a 2-D graph
The lines intersect at (-2/7,-12/7), so none of the choices listing a different intersection can be right. That leaves only (A).

Now you just have to check to see whether the lines pass through the named points.

No luck there. I suspect a typo in the equations.

To solve the system of equations by graphing, we need to plot the lines represented by each equation and find the point of intersection, which will give us the solution to the system.

Let's start with the first equation: x + y = -2
To graph this line, we can rearrange the equation to solve for y:
y = -x - 2

Now, we can choose some x-values, plug them into the equation, and find the corresponding y-values to plot the points on the graph. For simplicity, let's choose x = -3, 0, and 3.

For x = -3:
y = -(-3) - 2
y = 3 - 2
y = 1
So, we have the point (-3, 1).

For x = 0:
y = -0 - 2
y = -2
So, we have the point (0, -2).

For x = 3:
y = -3 - 2
y = -5
So, we have the point (3, -5).

Plotting these points on a graph, we can draw a line passing through them.

Now, let's move on to the second equation: y = 13x + 2
This equation is already in slope-intercept form, where the coefficient of x is the slope (13) and the constant term (2) is the y-intercept.

To graph this line, we can choose some x-values, plug them into the equation, and find the corresponding y-values. Again, let's choose x = -3, 0, and 3.

For x = -3:
y = 13(-3) + 2
y = -39 + 2
y = -37
So, we have the point (-3, -37).

For x = 0:
y = 13(0) + 2
y = 0 + 2
y = 2
So, we have the point (0, 2).

For x = 3:
y = 13(3) + 2
y = 39 + 2
y = 41
So, we have the point (3, 41).

Plotting these points on the same graph, we can draw a line passing through them.

The solution to the system of equations is the point where the two lines intersect. Looking at the options provided:

A. (6, 4) - This point is not on either of the two lines. It is not the correct solution.

B. (-3, 1) - This point matches one of the points we found when graphing the first equation. It is a possible solution, but we need to check if it also satisfies the second equation.

Plugging the values of x = -3 and y = 1 into the second equation:
1 = 13(-3) + 2
1 = -39 + 2
1 = -37 (not true)

So, the point (-3, 1) is not the solution to the system.

C. (3, 1) - This point is not on either of the two lines. It is not the correct solution.

D. (0, -2) - This point matches one of the points we found when graphing the first equation. It is a possible solution, but we need to check if it also satisfies the second equation.

Plugging the values of x = 0 and y = -2 into the second equation:
-2 = 13(0) + 2
-2 = 0 + 2
-2 = 2 (not true)

So, the point (0, -2) is not the solution to the system.

After careful analysis, none of the provided options (A, B, C, or D) represent the correct solution to the system.