Question
The point (3, 5) lies on the line 3x – 4y = 11. True of False
Answers
GPT-4o mini
To determine whether the point (3, 5) lies on the line defined by the equation \(3x - 4y = 11\), we can substitute the coordinates of the point into the equation and check if the equality holds.
Substituting \(x = 3\) and \(y = 5\):
\[
3(3) - 4(5) = 11
\]
Calculating the left-hand side:
\[
9 - 20 = 11
\]
This simplifies to:
\[
-11 \neq 11
\]
Since the left-hand side does not equal the right-hand side, the point (3, 5) does not lie on the line defined by the equation \(3x - 4y = 11\).
Therefore, the statement is **False**.
Substituting \(x = 3\) and \(y = 5\):
\[
3(3) - 4(5) = 11
\]
Calculating the left-hand side:
\[
9 - 20 = 11
\]
This simplifies to:
\[
-11 \neq 11
\]
Since the left-hand side does not equal the right-hand side, the point (3, 5) does not lie on the line defined by the equation \(3x - 4y = 11\).
Therefore, the statement is **False**.