Question

The statement explains why the ordered pair is a solution to the system of equations.

Is the statement true or false?

True False
The ordered pair (−3,−6) is a solution for the first equation, and it is a solution for the second equation. Therefore, (−3,−6)​ is a solution to the system of equations.

​−4x+y=65x−y=21​

Answer 1

To determine the truth of the statement regarding the ordered pair \((-3, -6)\) being a solution to the system of equations, we need to check if it satisfies both equations:

1. \( -4x + y = 6 \)
2. \( 5x - y = 21 \)

Let's substitute \((-3, -6)\) into both equations:

1. For the first equation:
\[
-4(-3) + (-6) = 6
\]
\[
12 - 6 = 6
\]
This simplifies to:
\[
6 = 6
\]
This equation is satisfied.

2. For the second equation:
\[
5(-3) - (-6) = 21
\]
\[
-15 + 6 = 21
\]
This simplifies to:
\[
-9 \neq 21
\]
This equation is **not** satisfied.

Since the ordered pair \((-3, -6)\) does not satisfy both equations, the statement is **False**.