solve the problem grafically, 4y=x+4, x=2/3y+8/3
see the solution at
http://www.wolframalpha.com/input/?i=solve+4y%3Dx%2B4%2C+x%3D2%2F3y%2B8%2F3+
To solve the system of equations graphically, we need to plot the lines represented by each equation on the same graph and then find the point of intersection, if any.
Let's solve the system of equations graphically:
Equation 1: 4y = x + 4
Equation 2: x = (2/3)y + (8/3)
For Equation 1, we can rearrange it to the slope-intercept form (y = mx + b):
y = (1/4)x + 1
For Equation 2, we can also rearrange it to the slope-intercept form:
y = (3/2)x - (4/3)
Now, let's plot these two lines on a graph:
1. Plotting Equation 1:
- Start by marking the y-intercept, which is 1. Place a point at (0, 1).
- Determine the slope, which is 1/4. This means that for every 4 units moved horizontally (to the right), we move 1 unit vertically (upwards).
- From the y-intercept, move 4 units to the right and 1 unit up. Place another point.
- Connect the two points with a straight line. This line represents Equation 1.
2. Plotting Equation 2:
- Start by marking the y-intercept, which is -4/3. Place a point at (0, -4/3).
- Determine the slope, which is 3/2. This means that for every 2 units moved horizontally (to the right), we move 3 units vertically (upwards).
- From the y-intercept, move 2 units to the right and 3 units up. Place another point.
- Connect the two points with a straight line. This line represents Equation 2.
Now, observe the graph and locate the point of intersection of the two lines, if there is one. This point represents the solution to the system of equations.
If the lines intersect at a specific point (x, y), then that point is the solution to the system of equations. If the lines are parallel and do not intersect, then there is no solution. If the lines coincide (overlapping), then there are infinitely many solutions.
By graphing the lines, you can visually identify the point of intersection, if it exists, and determine the solution to the system of equations.