1. Using the following system of equations : 4x +2x = 6 2x + y= 3
A: Find the solution(s) algebraically showing all work (4 pts)
B: State whether it is independent consistent, dependent consistent, or inconsistent. (2pts)
C: Demonstrate how to check the systems of solutions, showing all work. (4 pts)
A: Find the solution(s) algebraically showing all work (4 pts)
B: State whether it is independent consistent, dependent consistent, or inconsistent. (2pts)
C: Demonstrate how to check the systems of solutions, showing all work. (4 pts)
Two concerns about your post:
1. For the first equation, did you mean 4x + 2y = 6 ?
2. This is clearly an assignment which will be marked, since you are showing how many points each answer is worth.
We do not do a student's assignment for them.
Show your steps and the area where your difficulties arise and somebody will gladly help you.
Hint:
Isn't your first equation just double the 2nd ??
A: To find the solution(s) algebraically, we need to solve the given system of equations:
1) 4x + 2y = 6
2) 2x + y = 3
To eliminate the y variable, we can multiply equation 2 by -2 and add it to equation 1:
-4x - 2y = -6
2x + y = 3
----------------
-2x = -3
Now, we can solve for x by dividing both sides of the equation by -2:
-2x / -2 = -3 / -2
x = 3/2
x = 1.5
Next, substitute the value of x in either of the original equations to find the value of y. Let's use equation 2:
2(1.5) + y = 3
3 + y = 3
y = 3 - 3
y = 0
So, the solution to the system of equations is x = 1.5 and y = 0.
B: To determine whether the system is independent consistent, dependent consistent, or inconsistent, we can analyze the number of solutions.
Since we obtained a unique solution for both x and y, the system is independent consistent.
C: To check the validity of the solution, we substitute the values of x and y back into the original equations:
Equation 1: 4x + 2y = 6
4(1.5) + 2(0) = 6
6 + 0 = 6
6 = 6
Equation 2: 2x + y = 3
2(1.5) + 0 = 3
3 + 0 = 3
3 = 3
Both equations are true when x = 1.5 and y = 0, which confirms that the solution is correct.