Solve each system graphically. If a system has an infinite number of solutions, use set builder notation to write the solution set. If a system has no solution,
state this. x + y = 6
x - y = 4
I'm lost, Please Help!! Thank you
x+y=6
-(x-y=4)
________
2y=2
- - <divide both sides by 2, to get y
2 2
______
y=1
Set x+1=6
x=6-1=5
____Need to check
y=2 and x=5 if its true
--------
5+2=7 not 4
5-2=3 not 4
{No solution}
I meant to say at the end that
if:
x=5 and y=2
and you plug them into the 2 equations that answer are different.
x+y=6
(5)+(2)=7 , not true
x-y=4
(5)-(2)=3
Hope this helps
To solve the system of equations graphically, we need to graph each equation on the same coordinate plane and find the point(s) where the two graphs intersect. These intersection point(s) represent the solution(s) to the system.
Let's solve the system:
1) x + y = 6
2) x - y = 4
We'll solve equation 1) for y:
y = 6 - x
Now, let's create a table of values for each equation:
For equation 1):
When x = 0, y = 6 - 0 = 6. So we have the point (0, 6).
When x = 1, y = 6 - 1 = 5. So we have the point (1, 5).
When x = 2, y = 6 - 2 = 4. So we have the point (2, 4).
When x = 3, y = 6 - 3 = 3. So we have the point (3, 3).
When x = 4, y = 6 - 4 = 2. So we have the point (4, 2).
For equation 2):
When x = 0, y = 0 - 4 = -4. So we have the point (0, -4).
When x = 1, y = 1 - 4 = -3. So we have the point (1, -3).
When x = 2, y = 2 - 4 = -2. So we have the point (2, -2).
When x = 3, y = 3 - 4 = -1. So we have the point (3, -1).
When x = 4, y = 4 - 4 = 0. So we have the point (4, 0).
Now, let's plot these points on the graph:
|
6 | x x
|
5 | x
|
4 | x
|
3 | x
|
2 | x
|
1 |
|
0 |
|_____________________________
0 1 2 3 4
The first equation is represented by the red dots, and the second equation is represented by the blue dots. We can see that these two lines intersect at the point (5, 1).
So, the solution to the system of equations is x = 5 and y = 1.
Therefore, the solution set in set builder notation is {(x, y) | x = 5, y = 1}.
To solve the given system of linear equations graphically, we need to plot the two lines represented by the equations on the same coordinate plane. The point of intersection, if it exists, will give us the solution to the system.
Let's start by rearranging the equations in slope-intercept form (y = mx + c), where m represents the slope of the line and c is the y-intercept.
First equation: x + y = 6
Rearranging, we get y = 6 - x or y = -x + 6.
Second equation: x - y = 4
Rearranging, we get y = x - 4.
Now that we have both equations in slope-intercept form, we can proceed to plot them on a graph.
Step 1: Assign values to x and calculate corresponding y-values for each equation. To simplify this process, we can create a table:
For the first equation:
x | y
---------
0 | 6
1 | 5
2 | 4
3 | 3
For the second equation:
x | y
---------
0 | -4
1 | -3
2 | -2
3 | -1
Step 2: Plot the points obtained from the table for both equations on the same coordinate plane.
Step 3: Draw a straight line passing through each set of points. Ensure that the lines extend beyond the plotted points.
Step 4: Identify the point where the two lines intersect, if it exists.
Upon graphing, we can observe that the lines intersect at the point (5, 1). This means that (x, y) = (5, 1) is the solution to the given system of equations.
In set builder notation, the solution would be written as { (x, y) | x = 5 and y = 1 }.
Therefore, the given system of equations has a unique solution, and that solution is x = 5 and y = 1.