Determine whether the point \((-2, 1)\) lies on Line 1, Line 2, both, or neither.
Check if \((-2, 1)\) lies on Line 1: \(-9x + 11y = -8\).
Substitute \(x = -2\) and \(y = 1\) into Line 1:
\[
-9(-2) + 11(1) = 18 + 11 = 29 \neq -8.
\]
The point \((-2, 1)\) does not lie on Line 1.
Check if \((-2, 1)\) lies on Line 2: \(-4x + 9y = 17\).
Substitute \(x = -2\) and \(y = 1\) into Line 2:
\[
-4(-2) + 9(1) = 8 + 9 = 17.
\]
The point \((-2, 1)\) lies on Line 2.
The point \((-2, 1)\) lies on Line 2 only.
\(\boxed{\text{Line 2}}\)
Determine whether the point \((4, -6)\) lies on Line 1, Line 2, both, or neither.
Check if \((4, -6)\) lies on Line 1: \(-9x + 11y = -8\).
Substitute \(x = 4\) and \(y = -6\) into Line 1:
\[
-9(4) + 11(-6) = -36 - 66 = -102 \neq -8.
\]
The point \((4, -6)\) does not lie on Line 1.
Check if \((4, -6)\) lies on Line 2: \(-4x + 9y = 17\).
Substitute \(x = 4\) and \(y = -6\) into Line 2:
\[
-4(4) + 9(-6) = -16 - 54 = -70 \neq 17.
\]
The point \((4, -6)\) does not lie on Line 2.
The point \((4, -6)\) lies on neither line.
\(\boxed{\text{Neither Line}}\)
Determine whether the point \((-4, -4)\) lies on Line 1, Line 2, both, or neither.
Check if \((-4, -4)\) lies on Line 1: \(-9x + 11y = -8\).
Substitute \(x = -4\) and \(y = -4\) into Line 1:
\[
-9(-4) + 11(-4) = 36 - 44 = -8.
\]
The point \((-4, -4)\) lies on Line 1.
Check if \((-4, -4)\) lies on Line 2: \(-4x + 9y = 17\).
Substitute \(x = -4\) and \(y = -4\) into Line 2:
\[
-4(-4) + 9(-4) = 16 - 36 = -20 \neq 17.
\]
The point \((-4, -4)\) does not lie on Line 2.
The point \((-4, -4)\) lies on Line 1 only.
\(\boxed{\text{Line 1}}\)
The point \((-2, 1)\) lies on Line 2 only.
The point \((4, -6)\) lies on neither line.
The point \((-4, -4)\) lies on Line 1 only.