I made an error on the one before this because I did not enter the equations. Solve the system of equations by graphing Then classify the system as consistent or inconsistent __dependent or independent
8x-4y=-16 4y-8x=16
what would happen if you muliplied the first equation by -1 ?
So how many equations do you really have ?
What does your textbook or your notes say about this situation ?
To solve the system of equations by graphing, we will need to graph the two lines and determine their point of intersection.
Let's start by rearranging the equations into slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
Equation 1: 8x - 4y = -16
Rearranging, we get:
-4y = -8x - 16
Dividing by -4:
y = 2x + 4
Equation 2: 4y - 8x = 16
Rearranging, we get:
4y = 8x + 16
Dividing by 4:
y = 2x + 4
Now that we have both equations in slope-intercept form, we can graph them.
For Equation 1, the slope (m) is 2, and the y-intercept (b) is 4. Thus, we can plot the point (0, 4) on the graph and use the slope to find other points. For example, moving one unit to the right and two units up, we can plot the point (1, 6). Connect these points to graph the line.
For Equation 2, we observe that it is the same line as Equation 1. Both equations have the same slope and y-intercept. Therefore, when we graph Equation 2, it will overlap with Equation 1 exactly.
Now we can see that the two lines are the same and overlap perfectly. This means that the system of equations has infinitely many solutions. Therefore, the system is consistent and dependent.
In summary, to solve this system of equations:
1. Rearrange the equations in slope-intercept form (y = mx + b).
2. Graph the lines by plotting the y-intercept and using the slope to find other points.
3. Determine the point of intersection.
4. If the lines overlap perfectly, the system is consistent and dependent.