To determine if the point [tex]\((-1, 8)\)[/tex] is a point of intersection for the given lines, we need to check if [tex]\((-1, 8)\)[/tex] satisfies both equations. Here are the steps:
1. Verify the first equation:
The first equation is [tex]\(-x + 4y = 12\)[/tex].
Substituting [tex]\(x = -1\)[/tex] and [tex]\(y = 8\)[/tex] into the equation:
[tex]\[
-(-1) + 4 \cdot 8 = 1 + 32 = 33
\][/tex]
The left-hand side (33) does not equal the right-hand side (12). Therefore, the point [tex]\((-1, 8)\)[/tex] does not satisfy the first equation.
2. Verify the second equation:
The second equation is [tex]\(5x + y = 3\)[/tex].
Substituting [tex]\(x = -1\)[/tex] and [tex]\(y = 8\)[/tex] into the equation:
[tex]\[
5 \cdot (-1) + 8 = -5 + 8 = 3
\][/tex]
The left-hand side (3) equals the right-hand side (3). Therefore, the point [tex]\((-1, 8)\)[/tex] does satisfy the second equation.
Given that [tex]\((-1, 8)\)[/tex] does not satisfy the first equation but satisfies the second equation, we conclude that the point [tex]\((-1, 8)\)[/tex] is not a point of intersection of the two given lines.
Answer: No, [tex]\((-1, 8)\)[/tex] is not a point of intersection because it is not a solution to [tex]\(-x + 4y = 12\)[/tex].
