3x-9y=63

2x-6y=-18
Solve system of equations by graphing then classify as Independent on dependent and consistent or inconsistent?

Without any work, I can see that each line has a slope of 1/3.

So you will have two parallel lines, which of course will not meet.
So what classification would the system fall under?

Consistent and independent?

Yes, they are independent, because one equation cannot be derived from the other.

But they are inconsistent, since there is no solution.

To solve the system of equations by graphing, we will first need to rearrange each equation in slope-intercept form, which is y = mx + b. Once we have the equations in this form, we can graph them and determine their solutions.

Let's start with the first equation:
3x - 9y = 63
Rearranging, we get:
-9y = -3x + 63
Dividing both sides by -9, we have:
y = (1/3)x - 7

Now let's rearrange the second equation:
2x - 6y = -18
-6y = -2x - 18
Dividing both sides by -6, we get:
y = (1/3)x + 3

Now that we have both equations in slope-intercept form (y = mx + b), we can graph them.

To do this, create a coordinate plane and plot the points for each equation. We'll need to choose some x-values, calculate the corresponding y-values using the equations, and then plot those points.

For the first equation, you could choose at least two x-values (e.g., x = 0 and x = 6) and calculate the associated y-values:
For x = 0, y = (1/3)(0) - 7 = -7
For x = 6, y = (1/3)(6) - 7 = -5

Plotting the points (0, -7) and (6, -5) on the graph, we can draw a line that passes through both of these points.

For the second equation, follow the same process:
For x = 0, y = (1/3)(0) + 3 = 3
For x = 6, y = (1/3)(6) + 3 = 5

Plotting the points (0, 3) and (6, 5) on the graph, draw a line passing through these points as well.

Now, examine the graph. If the lines intersect at one point, the system is consistent, and there is a unique solution. If the lines are parallel and never intersect, the system is inconsistent, and there is no solution. If the lines coincide (overlap each other), the system is dependent, and there are infinitely many solutions.

Based on the graph of this system, if you find that the lines intersect at one point, then the system is consistent and has a unique solution. If the lines are parallel, then the system is inconsistent and has no solution. If the lines coincide (overlap), then the system is dependent and has infinitely many solutions.

Note: It's important to verify your answer by calculating the values of x and y from the equations to confirm that they satisfy both equations.