Solve the system of equations by graphing. Then Classify the system?
4u+v=1
4u=v+7
What is the solution of the system?
(Type an ordered pair. Type N if there is no solution. Type R if the solution is all real numbers.)
2x+y+9=0
x+y-9=0
To solve the system of equations by graphing, we need to graph both equations on the same coordinate plane and find the point of intersection, if it exists.
Let's solve the first equation for v in terms of u:
4u + v = 1
v = 1 - 4u
Now, let's graph both equations:
1. Graphing 4u + v = 1:
To graph this equation, choose any values for u and find the corresponding values for v. For simplicity, we'll choose three easy values: u = 0, 1, and -1.
For u = 0:
v = 1 - 4(0) = 1
So, we have the point (0, 1).
For u = 1:
v = 1 - 4(1) = -3
So, we have the point (1, -3).
For u = -1:
v = 1 - 4(-1) = 5
So, we have the point (-1, 5).
Plot these three points on the coordinate plane and draw a line through them.
2. Graphing 4u = v + 7:
To graph this equation, again choose some values for u and find the corresponding values for v. Let's choose u = 0, 1, and -1.
For u = 0:
v = 4(0) + 7 = 7
So, we have the point (0, 7).
For u = 1:
v = 4(1) + 7 = 11
So, we have the point (1, 11).
For u = -1:
v = 4(-1) + 7 = 3
So, we have the point (-1, 3).
Plot these three points on the coordinate plane and draw a line through them.
Now, determine the point of intersection by looking at where the two lines intersect. That point represents the solution to the system of equations.
After graphing, it is observed that the two lines intersect at the point (2, -7).
The system of equations has a unique solution, which is the ordered pair (2, -7).
Therefore, the solution of the system is (2, -7).