Question

ALgebra

Answer 1

@mathstudent55 I need help here

Answer 2

1. Using the following system of equations : 4x +2y = 6
2x + y= 3
A: Find the solution(s) algebraically showing all work (4pts)
B: State whether it is independent consistent, dependent consistent, or inconsistent. (2pts)

C: Demonstrate how to check the systems of solutions, showing all work. (4pts)
A: Find the solution(s) algebraically showing all work (4pts)


B: State whether it is independent consistent, dependent consistent, or inconsistent. (2pts)

C: Demonstrate how to check the systems of solutions, showing all work. (4pts)

Answer 3

@SouthernBelle730 here it is, there are 4 more questions but his is the first one

Answer 4

@mathstudent55 @Math2400

Answer 5

Your equations:
\[\begin{array}{lcl} 4x + 2y & = & 6 \\ 2x + y & = & 3 \end{array}\]
We can try to replace the second equation by multiplying the first equation by -1/2, then adding it to the second equation. This may be a good place to start because -2x + 2x = 0 (i.e. we may be able to eliminate a variable, making this simpler)
\[\begin{array}{ccc} -\frac{1}{2}\left( 4x + 2y \right) & = & -\frac{1}{2} \times 6 \\ 2x + y & = & 3\end{array}\]
If we add (you can do it yourself to check the algebra), we end up replacing the second equation and the system of equations becomes
\[\begin{array}{lcl} 4x + 2y & = & 6 \\ 0x + 0y & = & 0 \end{array}\]
Now does this represent a system that is independent consistent, dependent consistent, or inconsistent?

Answer 6

dependant consistent?

Answer 7

yep! Think about that last equation
\[0x + 0y = 0\]
Any x and any y will satisfy this equation, so there are infinitely many solutions (dependent). The fact that solutions exist makes this a consistent system.

Answer 8

brb gotta use the ladies room

Answer 9

ok @DisplayError im back

Answer 10

@mathstudent55

Answer 11

@mathmate hey long time no see, can you help me in these?

Answer 12

Hi @mely1014
Long time no see. Guess you're afk.
You already got the correct answer for part b without showing work for part A.
Suppose part A is what you need.
Hint:
When one equation equals the exact multiple of another, the two form a system of consistent but dependent solution.
For example: 2x+y=5 and 4x+2y=10 form a dependent system because twice the first equation gives exactly the second. It's consistent because twice 5 gives 10.
Geometrically, the two lines are parallel, but are coincident. Algebraically, there is an infinite number of solutions because 2x+y=5 means y=2x+5.
Any point that satisfies (x, 2x+5) lies on the line, hence it is a solution.

Answer 13

ok so this is a hint for part A right?

Answer 14

@dayani.laforest

Answer 15

Yes, it is a hint, and it is almost the answer.
You need to check if the given problem falls into this category.