solve the system of equation by graphing then classify the system as consistent or inconsistent and as dependent or independent
8x-4y= -20
4y-8x= 20
i don't understand it.
To solve the system of equations by graphing, you need to plot the two equations on a graph and find the point where they intersect. This point represents the solution to the system.
Let's start with the first equation: 8x - 4y = -20. To plot this equation, you'll want to rearrange it in terms of y:
8x - 4y = -20
-4y = -8x - 20
y = 2x + 5
Now, choose some values of x, plug them into the equation, and calculate the corresponding y-values. Once you have a few points, plot them on a graph.
Next, let's move on to the second equation: 4y - 8x = 20. Rearrange this equation in terms of y:
4y - 8x = 20
4y = 8x + 20
y = 2x + 5
You'll notice that this equation is the same as the first one. Therefore, the two equations represent the same line on the graph. In this case, the system of equations is a dependent system because the two equations are equivalent.
When you graph these equations, you'll see that the lines overlap each other perfectly. This means that there are infinitely many solutions to the system, and it is consistent.
So, to summarize:
- The system of equations is a dependent system because the two equations represent the same line.
- The system is consistent because the lines overlap.
- There are infinitely many solutions to the system.