Graph the two equations to solve the system. Write the ordered pair solution like this (1,2) with no spaces, or write no solution or infinitely many solutions.
1/2 x - 2y = 4 and 4y - x = -8
Do this the same way as shown in your 1st post.
To graph the two equations, we first need to convert them into slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
Let's start with the first equation:
1/2x - 2y = 4
Move the 1/2x term to the other side by subtracting it from both sides:
-2y = -1/2x + 4
Next, divide both sides by -2 to isolate y:
y = 1/4x - 2
Now we have the equation in slope-intercept form.
For the second equation:
4y - x = -8
Let's move the -x term to the other side by adding x to both sides:
4y = x - 8
Now, divide both sides by 4 to isolate y:
y = 1/4x - 2
As you can see, both equations have the same slope-intercept form, y = 1/4x - 2. This means that both equations represent parallel lines.
To graph the lines, start by plotting the y-intercept, which is -2. Then, use the slope (1/4) to find other points on the line. Since the slope is positive, you can move up 1 unit and right 4 units from the y-intercept to find another point. Connect the points to form a straight line.
Using this process, we will end up with two parallel lines. Since parallel lines do not intersect, there is no solution to this system of equations. Therefore, the solution is "no solution."