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
You should be able to read the solution.
http://www.wolframalpha.com/input/?i=plot+3x+%2B+2y+%3D+5+%2C+4x+−+3y+%3D+1
The function h(x) =1/98x^2 describe the height of part of a roller coaster track where x is the horizontal distance in feet from the center of this section of the track the towers that support this part of the track are the same height and are 150ft apart what is the best estimate of the height of the towers
To solve a system of linear equations by graphing, we need to plot the graphs of both equations on the same coordinate plane and find the point(s) where the lines intersect.
Let's solve the system of equations:
1) 3x + 2y = 5
2) 4x - 3y = 1
Step 1: Solve Equation 1 for y
3x + 2y = 5
2y = 5 - 3x
y = (5 - 3x) / 2
Step 2: Solve Equation 2 for y
4x - 3y = 1
-3y = 1 - 4x
y = (4x - 1) / 3
Now, we have both equations in slope-intercept form (y = mx + b).
Step 3: Graph the equations on a coordinate plane:
To graph the first equation (y = (5 - 3x) / 2), we can use the following points to plot the line:
- Choose three arbitrary values for x.
- Substitute each x-value into the equation to find the corresponding y-coordinate.
- Plot the points and draw a line through them.
For example:
When x = 0, y = (5 - 3(0)) / 2 = 5 / 2 = 2.5
When x = 1, y = (5 - 3(1)) / 2 = 2 / 2 = 1
When x = 2, y = (5 - 3(2)) / 2 = -1 / 2 = -0.5
Plot these points and draw a line through them.
Next, we will graph the second equation (y = (4x - 1) / 3) using the same method:
When x = 0, y = (4(0) - 1) / 3 = -1/3
When x = 1, y = (4(1) - 1) / 3 = 3/3 = 1
When x = 2, y = (4(2) - 1) / 3 = 7/3
Plot these points and draw a line through them.
Step 4: Find the point(s) of intersection
Locate the point(s) where the two lines intersect on the graph. If there is a point, then the system has a unique solution and is consistent. If the lines do not intersect or if they overlap completely, then the system is either inconsistent or dependent.
In this case, it appears that the lines intersect at a single point (approximately (0.9, 1.2) or (0.9, 1.3) depending on the accuracy of the graph). Therefore, the system has a unique solution, and it is consistent.
To summarize: The solution to the system is x ≈ 0.9 and y ≈ 1.2 (or y ≈ 1.3).