solve the following system of equations by graphing if the system is inconsistent or the equations are dependent
x+2y=8 and 2x+4y=28
To solve the system of equations by graphing, we will need to plot the lines represented by the equations and find the point where they intersect (if they do). Let's graph the equations one by one:
1) x + 2y = 8
To find the x-intercept, we set y = 0:
x + 2(0) = 8
x = 8
So, the x-intercept is at (8, 0).
To find the y-intercept, we set x = 0:
0 + 2y = 8
2y = 8
y = 4
So, the y-intercept is at (0, 4).
Plotting the x-intercept (8, 0) and y-intercept (0, 4), we can draw a line passing through these two points.
2) 2x + 4y = 28
To find the x-intercept, we set y = 0:
2x + 4(0) = 28
2x = 28
x = 14
So, the x-intercept is at (14, 0).
To find the y-intercept, we set x = 0:
2(0) + 4y = 28
4y = 28
y = 7
So, the y-intercept is at (0, 7).
Plotting the x-intercept (14, 0) and y-intercept (0, 7), we can draw a line passing through these two points.
Graphing both lines, we have:
```
y
^
| .
| .
| x
| .
| .
| .
------------------------> x
```
The lines represented by the equations x + 2y = 8 and 2x + 4y = 28 are coincident, meaning they are the same line. Therefore, the system of equations is dependent.