Question

Which statement justifies the given ordered pair as a solution to the system of equations?

​(−1, −13)
​
{y=3x−10y=−2x−15



Responses

{−1=3(−13)−10−1=−2(−13)−15
A system of equations. First equation negative 1 equals 3 left parenthesis negative 13 right parenthesis minus 10. Second equation negative 1 equals negative 2 left parenthesis negative 13 right parenthesis minus 15.

{13=3(1)−1013=−2(1)−15
A system of equations. First equation 13 equals 3 left parenthesis 1 right parenthesis minus 10. Second equation 13 equals negative 2 left parenthesis 1 right parenthesis minus 15.

{1=3(13)−101=−2(13)−15
A system of equations. First equation 1 equals 3 left parenthesis 13 right parenthesis minus 10. Second equation 1 equals negative 2 left parenthesis 13 right parenthesis minus 15.

{−13=3(−1)−10−13=−2(−1)−15

Answer 1

To determine which statement correctly justifies the given ordered pair \((-1, -13)\) as a solution to the system of equations

\[
\begin{cases}
y = 3x - 10 \\
y = -2x - 15
\end{cases}
\]

we will substitute \(x = -1\) and \(y = -13\) into both equations.

1. For the first equation \(y = 3x - 10\):
\[
-13 = 3(-1) - 10
\]
\[
-13 = -3 - 10
\]
\[
-13 = -13 \quad \text{(True)}
\]

2. For the second equation \(y = -2x - 15\):
\[
-13 = -2(-1) - 15
\]
\[
-13 = 2 - 15
\]
\[
-13 = -13 \quad \text{(True)}
\]

Now we check the responses. The correct justification should show the substitutions correctly:

- The option that matches our calculations is:

\[
{-13=3(-1)-10 \\
-13=-2(-1)-15}
\]

So the correct statement is:

**{−13=3(−1)−10−13=−2(−1)−15}**

This statement correctly demonstrates that the ordered pair \((-1, -13)\) satisfies both equations in the system.