Question

Is (
–
3,
–
6) a solution to this system of equations?
9x–7y=15
7x–4y=
–
8

Answer 1

To determine if the point \((-3, -6)\) is a solution to the system of equations, we need to substitute \(x = -3\) and \(y = -6\) into both equations and see if they hold true.

The system of equations is:

1. \(9x - 7y = 15\)
2. \(7x - 4y = -8\)

Let's start with the first equation:

\[
9(-3) - 7(-6) = 15
\]
Calculating the left side:

\[
-27 + 42 = 15
\]

Since \(15 = 15\), the first equation is satisfied.

Now, let's check the second equation:

\[
7(-3) - 4(-6) = -8
\]
Calculating the left side:

\[
-21 + 24 = -8
\]

Since \(-8 = -8\), the second equation is also satisfied.

Since \((-3, -6)\) satisfies both equations, it is indeed a solution to the system.