Question
Use substitution to solve the system of equations. How many solutions are there?
12
x − 13
y = 5
x = 23
y + 10
There are no solutions.
There is one solution.
There are infinitely many solutions.
It is not possible to determine the number of solutions.
12
x − 13
y = 5
x = 23
y + 10
There are no solutions.
There is one solution.
There are infinitely many solutions.
It is not possible to determine the number of solutions.
Answers
Answered by
GPT-4o mini
To solve the given system of equations using substitution, we first need to clearly write down the equations. From your format, it seems like we have the following two equations:
1. \( 12x - 13y = 5 \)
2. \( x = 23 \)
Now, we will substitute the value of \( x = 23 \) into the first equation:
\[
12(23) - 13y = 5
\]
Calculating \( 12(23) \):
\[
276 - 13y = 5
\]
Next, we can solve for \( y \):
\[
-13y = 5 - 276
\]
\[
-13y = -271
\]
\[
y = \frac{-271}{-13} = 20.846153846153847
\]
Thus, we have \( x = 23 \) and \( y \approx 20.85 \).
Since we are able to find specific values for both \( x \) and \( y \), we can conclude that there is **one solution** to the system of equations.
Final answer:
There is one solution.
1. \( 12x - 13y = 5 \)
2. \( x = 23 \)
Now, we will substitute the value of \( x = 23 \) into the first equation:
\[
12(23) - 13y = 5
\]
Calculating \( 12(23) \):
\[
276 - 13y = 5
\]
Next, we can solve for \( y \):
\[
-13y = 5 - 276
\]
\[
-13y = -271
\]
\[
y = \frac{-271}{-13} = 20.846153846153847
\]
Thus, we have \( x = 23 \) and \( y \approx 20.85 \).
Since we are able to find specific values for both \( x \) and \( y \), we can conclude that there is **one solution** to the system of equations.
Final answer:
There is one solution.