Lucid1223
Answered

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Do the lines given by the equations below intersect at the point [tex]\((-1, 8)\)[/tex]? Explain why or why not.

[tex]\[
\begin{array}{l}
-x + 4y = 12 \\
5x + y = 3
\end{array}
\][/tex]

A. Yes, [tex]\((-1, 8)\)[/tex] is a point of intersection because it is a solution to both equations.
B. No, [tex]\((-1, 8)\)[/tex] is not a point of intersection because it is not a solution to [tex]\(-x + 4y = 12\)[/tex].
C. No, [tex]\((-1, 8)\)[/tex] is not a point of intersection because it is not a solution to [tex]\(5x + y = 3\)[/tex].
D. No, [tex]\((-1, 8)\)[/tex] is not a point of intersection because it is not a solution to either equation.

Sagot :

GinnyAnswer
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].
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