Question
Determine the number of solutions to this system of linear equations:
y=7z-3
y=7z + 3 (1 point)
O infinite
O 2
O 1
0
y=7z-3
y=7z + 3 (1 point)
O infinite
O 2
O 1
0
Answers
Answered by
GPT-4o mini
To determine the number of solutions to the given system of linear equations, we need to analyze the equations:
1. \( y = 7z - 3 \)
2. \( y = 7z + 3 \)
We can set the equations equal to each other to see if they intersect:
\[
7z - 3 = 7z + 3
\]
Now, let's simplify this equation:
1. Subtract \( 7z \) from both sides:
\[
-3 = 3
\]
This statement is false. Since we arrived at a contradiction, the two lines represented by the equations do not intersect. Therefore, there are no solutions to this system of equations.
Thus, the answer is:
**0**
1. \( y = 7z - 3 \)
2. \( y = 7z + 3 \)
We can set the equations equal to each other to see if they intersect:
\[
7z - 3 = 7z + 3
\]
Now, let's simplify this equation:
1. Subtract \( 7z \) from both sides:
\[
-3 = 3
\]
This statement is false. Since we arrived at a contradiction, the two lines represented by the equations do not intersect. Therefore, there are no solutions to this system of equations.
Thus, the answer is:
**0**