Final answer:
To write the equations in slope-intercept form, x - 2y = 8 can be represented as y = (1/2)x - 4 and -2x + 4y = -16 can be represented as y = (1/2)x - 4. The system has infinitely many solutions, and the graph of the system will be a line.
Step-by-step explanation:
To write the equation x - 2y = 8 in slope-intercept form, y = mx + b, we need to isolate y. So, we can start by moving x to the other side of the equation:
x - 2y + 2y = 8 + 2y
x = 2y + 8
Now, we can solve for y by dividing both sides of the equation by 2:
y = (1/2)x - 4
Therefore, x - 2y = 8 in slope-intercept form is y = (1/2)x - 4.
To write the equation -2x + 4y = -16 in slope-intercept form, we need to isolate y as well. Here's the process:
-2x + 4y = -16
4y = 2x - 16
y = (1/2)x - 4
Therefore, -2x + 4y = -16 in slope-intercept form is y = (1/2)x - 4.
Since both equations have the same slope and y-intercept, they represent the same line. Therefore, the system will have infinitely many solutions, and the graph of the system will be a line.
Learn more about slope-intercept form of equations