Question

Determine whether left parenthesis 5 comma 1 right parenthesis is a solution of the​ system:
3 x minus y
equals
14
negative x plus 3 y
equals
negative 2
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Part 1
Is left parenthesis 5 comma 1 right parenthesis a solution of the​ system?
Yes
No

Answer 1

To determine if the point \( (5, 1) \) is a solution of the given system of equations, we need to substitute \( x = 5 \) and \( y = 1 \) into both equations and see if they hold true.

The system of equations is:
1. \( 3x - y = 14 \)
2. \( -x + 3y = -2 \)

Let's substitute \( x = 5 \) and \( y = 1 \) into the first equation:

1. \( 3(5) - 1 = 14 \)

Calculating that gives:

\[ 15 - 1 = 14 \]

This simplifies to:

\[ 14 = 14 \] (True)

Now, let's check the second equation:

2. \( -5 + 3(1) = -2 \)

Calculating that gives:

\[ -5 + 3 = -2 \]

This simplifies to:

\[ -2 = -2 \] (True)

Since both equations hold true when substituting \( (5, 1) \), we can conclude that:

**Yes, \( (5, 1) \) is a solution of the system.**