Solve the system of equations by graphing. Then classify the system.

y=-x-13
5x-4y=-20

What is the solution of the system?
a)The solution is___?
b)There are infinitely many solutions
c)There is no solution

Is the system consistent or inconsistent?
a)inconsistent
b)consistent

Are the equations dependent or independent?
a)dependent
b)independent

since the lines are not the same or parallel, then they have a single solution.

I'm sure you can come up with it.

So, the equations are independent and consistent.

dependent means they are the same line
inconsistent means they are parallel lines.

To solve the system of equations by graphing, we'll start by graphing each equation on the same coordinate plane:

1) The first equation is y = -x - 13. To graph this equation, start by plotting the y-intercept at (0, -13). Then, use the slope of -1 to find another point. Since the slope is -1, it means that for every 1 unit increase in x, y will decrease by 1 unit. So from the point (0, -13), go down 1 unit and right 1 unit to find another point. Connect the two points to graph the line.

2) The second equation is 5x - 4y = -20. To graph this equation, rearrange it in slope-intercept form y = mx + b. Subtract 5x from both sides and divide by -4 to get y = (5/4)x + 5. The y-intercept is (0, 5), and using the slope of 5/4, go up 5 units and right 4 units from the y-intercept to find another point. Connect the two points to graph the line.

After graphing both lines, we can visually determine the intersection point as the solution to the system of equations.

Solution: The solution of the system is the point where the two lines intersect. In this case, it appears that the lines intersect at the point (-8, 5).

Now let's classify the system:

a) The solution is not a good option since it requires filling in the blank.
b) There are infinitely many solutions when the two lines in the system overlap each other. In this case, it's not the scenario.
c) There is no solution when the lines are parallel and do not intersect. In this case, since the lines intersect, there is a solution, so option c) is not the answer.

The system is consistent when there is a solution, and inconsistent when there is no solution.

a) The system is inconsistent is incorrect since we found a solution.
b) The system is consistent is the correct classification.

The equations are said to be dependent if they represent the same line, and independent if they are different lines.

a) The equations are dependent is incorrect since the lines are different.
b) The equations are independent is the correct classification.

In summary, the solution of the system is (-8, 5). The system is consistent, and the equations are independent.