Asked by hehehe
How many solutions does the system of equations have?
8x−6y=48
8x+6y=48
(1 point)
Responses
infinite
infinite
one
one
none
none
two
8x−6y=48
8x+6y=48
(1 point)
Responses
infinite
infinite
one
one
none
none
two
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine the number of solutions for the given system of equations, we can analyze the equations directly. The system is:
1. \( 8x - 6y = 48 \) (Equation 1)
2. \( 8x + 6y = 48 \) (Equation 2)
We can solve this system by using the method of elimination or substitution. Let's add the two equations together:
\[
(8x - 6y) + (8x + 6y) = 48 + 48
\]
This simplifies to:
\[
16x = 96
\]
Now, dividing both sides by 16:
\[
x = 6
\]
Now that we have a value for \(x\), we can substitute it back into either equation to find \(y\). Let's use Equation 1:
\[
8(6) - 6y = 48
\]
This simplifies to:
\[
48 - 6y = 48
\]
Subtracting 48 from both sides gives:
\[
-6y = 0
\]
Dividing by -6:
\[
y = 0
\]
We found a unique solution: \( (6, 0) \).
Since we have found a specific value for both variables, the system has exactly **one** solution.
So, the answer is **one**.
1. \( 8x - 6y = 48 \) (Equation 1)
2. \( 8x + 6y = 48 \) (Equation 2)
We can solve this system by using the method of elimination or substitution. Let's add the two equations together:
\[
(8x - 6y) + (8x + 6y) = 48 + 48
\]
This simplifies to:
\[
16x = 96
\]
Now, dividing both sides by 16:
\[
x = 6
\]
Now that we have a value for \(x\), we can substitute it back into either equation to find \(y\). Let's use Equation 1:
\[
8(6) - 6y = 48
\]
This simplifies to:
\[
48 - 6y = 48
\]
Subtracting 48 from both sides gives:
\[
-6y = 0
\]
Dividing by -6:
\[
y = 0
\]
We found a unique solution: \( (6, 0) \).
Since we have found a specific value for both variables, the system has exactly **one** solution.
So, the answer is **one**.
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