Help!! I am having difficulty with a problem for hours now and if I could get some help, my head might stop pounding.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. 2x - y = 4, 5x - y =13
Draw a Cartesian coordinate system.
Now :
2 x - y = 4
for x = 0
2 x - y = 4
2 * 0 - y = 4
- y = 4 Multiply both sides by - 1
y = - 4
This is first point ( x = 0 , y = 4 )
for y = 0
2 x - y = 4
2 x - 0 = 4
2 x = 4 Divide both sides by 2
x = 2
This is second point ( x = 2 , y = 0 )
Draw straight line between this two point.
5 x - y = 13
for x = 0
5 x - y = 13
5 * 0 - y = 13
- y = 13 Multiply both sides by - 1
y = - 13
This is first point ( x = 0 , y = - 13 )
for y = 0
5 x - y = 13
5 x - 0 = 13
5 x = 13 Divide both sides by 5
x = 13 / 5 = 2.6
This is second point ( x = 2.6 , y = 0 )
Draw straight line between this two point.
Intersection point of this two lines is the solution.
Coordinate of solution:
x = 3 , y = 2
You can write the solution like :
( 3 , 2 )
If you want to see graph in google type :
function graphs online
When you see list of results click on :
Draw Function Graphs - Plotter - Rechneronline
When page be open in blue rectangle type :
2 x - 4
In gray rectangle type :
5 x - 13
Set:
Range y-axis from - 15 to 5
and click option :
Draw
You will see graphs
Remark:
2 x - y = 4
is same
y = 2 x - 4
5 x - y = 13
is same
y = 5 x - 13
To solve the system of equations graphically, we will plot the equations on a graph and find the point of intersection if it exists. Let's solve the given system:
The first equation is 2x - y = 4.
Let's rearrange it to solve for y:
y = 2x - 4.
The second equation is 5x - y = 13.
Rearranging it, we get:
y = 5x - 13.
Now, we can visualize these equations on a graph by plotting a few points on each line and connecting them.
For the first equation, let's choose arbitrary values for x and calculate y:
When x = 0, y = 2(0) - 4 = -4. This gives us the point (0, -4).
When x = 1, y = 2(1) - 4 = -2. This gives us the point (1, -2).
For the second equation:
When x = 0, y = 5(0) - 13 = -13. This gives us the point (0, -13).
When x = 1, y = 5(1) - 13 = -8. This gives us the point (1, -8).
Now, plot these points on the graph:
``
|
|
|
| x
| xx
| x x x
| x x
| x
|___________________
-4 -2 0 -13 -8
``
The lines intersect at the point (2, 0). Therefore, the solution to this system of equations is x = 2 and y = 0.
In set builder notation, we can express the solution set as {(x, y) | x = 2, y = 0}.