Solve the system by graphing. (If the system is inconsistent, enter INCONSISTENT. If the system is dependent, enter DEPENDENT.)
3x+2y=5
4x-3y=1
I have try dependent and inconsistent and either work. What am I doing wrong.
Thank you
You should have definitions for
dependent, independent, and incosistent.
if there is a unique solution , the system would be
independent.
since the two lines have different slopes, they MUST intersect in a point, thus independent
Wolfram is great ...
http://www.wolframalpha.com/input/?i=plot+3x%2B2y%3D5+%2C+4x-3y%3D1+
To solve the system by graphing, you need to follow these steps:
1. Solve each equation for y in terms of x.
Equation 1: 3x + 2y = 5
y = (5 - 3x) / 2
Equation 2: 4x - 3y = 1
y = (4x - 1) / 3
2. Create a graph with x and y as the axes.
3. Plot the points for each equation by substituting different x values into the corresponding equation to find the y value. For example, you can choose x = 0, x = 1, x = 2, etc., and calculate the y values.
4. Connect the plotted points for each equation with a straight line.
5. Check the point of intersection between the two lines on the graph. If there is a unique point of intersection, then the system is consistent and independent, which means there is a single solution. However, if the lines are parallel and never intersect, the system is inconsistent and has no solutions. If the lines coincide or overlap, the system is dependent and has infinite solutions.
Now, let's solve the given system of equations using the graphing method:
1. Solve the equations for y:
Equation 1: y = (5 - 3x) / 2
Equation 2: y = (4x - 1) / 3
2. Graph the lines representing each equation on the same graph.
3. Find the point of intersection, if any.
In this particular example, let's go through the steps together and see where the issue might be:
1. Solving for y:
Equation 1: y = (5 - 3x) / 2
Equation 2: y = (4x - 1) / 3
2. Creating a graph:
Plot the points for both equations by substituting x values to find corresponding y values.
3. Connecting the plotted points for each equation with a straight line.
4. Check for the point of intersection between the two lines.
If you are not finding a point of intersection, it might be a good idea to double-check your calculations and ensure that you have accurately graphed the equations. Pay special attention to any negative signs, fractions, and decimal places, as they can lead to errors.
If the lines are parallel and never intersect, the system is inconsistent, indicating that there are no solutions.
If the lines coincide or overlap, the system is dependent, which means there are infinitely many solutions.
I hope this helps you solve the system by graphing. If you are still having trouble, please feel free to provide the plotted points so that I can assist you further.