Question

Determine whether the given ordered pair is a solution of the system of equations. Remember to use alphabetically ordered variables.
​(2​,negative 1​);
negative 3yequals
xplus1
5yequals
4 x minus 13

Answer 1

To determine whether the ordered pair \((2, -1)\) is a solution to the system of equations given by:

1. \(-3y = x + 1\)
2. \(5y = 4x - 13\)

we'll substitute \(x = 2\) and \(y = -1\) into both equations.

**1. Testing the first equation: \(-3y = x + 1\)**

Substituting \(x = 2\) and \(y = -1\):

\[
-3(-1) = 2 + 1
\]

Calculating the left side:

\[
3 = 2 + 1
\]

Calculating the right side:

\[
3 = 3
\]

This equation holds true.

**2. Testing the second equation: \(5y = 4x - 13\)**

Substituting \(x = 2\) and \(y = -1\):

\[
5(-1) = 4(2) - 13
\]

Calculating the left side:

\[
-5 = 8 - 13
\]

Calculating the right side:

\[
-5 = -5
\]

This equation also holds true.

Since the ordered pair \((2, -1)\) satisfies both equations, it is indeed a solution to the system of equations.