Question
Solve the system of linear equations, if possible. State any solutions and classify each system
as consistent independent, consistent dependent, or inconsistent.
If not possible, enter
(a) The system of equations is:
Consistent dependent.
Inconsistent.
Consistent independent.
(b) The solution to the system is
as consistent independent, consistent dependent, or inconsistent.
If not possible, enter
(a) The system of equations is:
Consistent dependent.
Inconsistent.
Consistent independent.
(b) The solution to the system is
Ask by Dawson May. in the United States
Mar 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The system is consistent and dependent. The solutions are:
where
Solution
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Extra Insights
To solve the given system of equations, we can represent it as an augmented matrix and proceed with a row reduction method.
The equations are:
Arranging it into an augmented matrix, we have:
Now, we would apply row operations to reduce it:
- Replace Row 2 by Row 2 + 3 * Row 1.
- Replace Row 3 by Row 3 - 5 * Row 1.
After performing those operations, we get:
Next, we simplify Row 2 and Row 3 further.
After continuing the row operations and reaching a final reduced form, we eventually notice that the system yields a dependent scenario, leading us to express the variables in terms of one another.
Ultimately, the conclusion shows:
(a) The system of equations is: Consistent dependent.
(b) To find the solution, we can express
Let
Then, from the first equation:
Let
Then, from the first equation:
-
From the second: -
Rearranging these gives two equations that can be solved in terms of
So you might arrive at:
-
-
, and then substitute to find .
After calculations, you could say:
This means:
The solution to the system is
Have fun exploring how these dimensions of algebra weave together! Remember, linear systems can be full of surprises, just like a bake-off where not every cake rises!
