Question

Determine whether the given ordered pair is a solution of the system of equations. Remember to use alphabetically ordered variables.
​(13​,negative 5​);
negative 3yequals
xplus2
3yequals
6 x plus 63

Answer 1

To determine whether the ordered pair \((13, -5)\) is a solution to the system of equations:

1. The first equation is:
\[
-3y = x + 2
\]

2. The second equation is:
\[
3y = 6x + 63
\]

We will substitute \(x = 13\) and \(y = -5\) into both equations.

### Checking the first equation:
Substituting \(x = 13\) and \(y = -5\) into \(-3y = x + 2\):
\[
-3(-5) = 13 + 2
\]
Calculating both sides:
\[
15 = 15
\]
The first equation holds true.

### Checking the second equation:
Substituting \(x = 13\) and \(y = -5\) into \(3y = 6x + 63\):
\[
3(-5) = 6(13) + 63
\]
Calculating both sides:
\[
-15 = 78 + 63
\]
\[
-15 = 141
\]
This statement is false.

Since the second equation does not hold true, the ordered pair \((13, -5)\) is **not** a solution to the system of equations.