Question

Is (
–
9,
–
10) a solution to this system of equations?
17x–17y=17
6x–4y=
–
14

Answer 1

To determine if the point \((-9, -10)\) is a solution to the given system of equations, we can substitute \(x = -9\) and \(y = -10\) into both equations and check if they hold true.

The given equations are:

1. \(17x - 17y = 17\)
2. \(6x - 4y = -14\)

Let's check the first equation:

\[
17(-9) - 17(-10) = 17
\]
Calculating the left side:

\[
-153 + 170 = 17
\]

This simplifies to:

\[
17 = 17
\]

So the first equation is satisfied.

Now let's check the second equation:

\[
6(-9) - 4(-10) = -14
\]
Calculating the left side:

\[
-54 + 40 = -14
\]

This simplifies to:

\[
-14 = -14
\]

So the second equation is also satisfied.

Since both equations are satisfied, the point \((-9, -10)\) is indeed a solution to the system of equations.