Question
Solving Systems of Equations by Graphing Quick Check
2 of 52 of 5 Items
Question
Is (−2, 6) a solution to the system of these linear equations: x+2y=10 and 3x+y=0 ? Why?(1 point)
Responses
No, because the graphs don’t intersect at (−2, 6).
No, because the graphs don’t intersect at left parenthesis negative 2 comma 6 right parenthesis .
Yes, because the graphs don’t intersect at (−2, 6).
Yes, because the graphs don’t intersect at left parenthesis negative 2 comma 6 right parenthesis .
Yes, because the graphs intersect at (−2, 6).
Yes, because the graphs intersect at left parenthesis negative 2 comma 6 right parenthesis .
No, because the graphs intersect at (−2, 6).
2 of 52 of 5 Items
Question
Is (−2, 6) a solution to the system of these linear equations: x+2y=10 and 3x+y=0 ? Why?(1 point)
Responses
No, because the graphs don’t intersect at (−2, 6).
No, because the graphs don’t intersect at left parenthesis negative 2 comma 6 right parenthesis .
Yes, because the graphs don’t intersect at (−2, 6).
Yes, because the graphs don’t intersect at left parenthesis negative 2 comma 6 right parenthesis .
Yes, because the graphs intersect at (−2, 6).
Yes, because the graphs intersect at left parenthesis negative 2 comma 6 right parenthesis .
No, because the graphs intersect at (−2, 6).
Answers
GPT-4o mini
To determine if \((-2, 6)\) is a solution to the system of equations given by \(x + 2y = 10\) and \(3x + y = 0\), we can substitute the coordinates of the point into both equations:
1. **Substituting into the first equation \(x + 2y = 10\)**:
\[
-2 + 2(6) = -2 + 12 = 10
\]
This equation is satisfied.
2. **Substituting into the second equation \(3x + y = 0\)**:
\[
3(-2) + 6 = -6 + 6 = 0
\]
This equation is also satisfied.
Since both equations are satisfied by the coordinates \((-2, 6)\), we conclude that \((-2, 6)\) is indeed a solution to the system of equations.
Therefore, the correct response is:
**Yes, because the graphs intersect at (−2, 6).**
1. **Substituting into the first equation \(x + 2y = 10\)**:
\[
-2 + 2(6) = -2 + 12 = 10
\]
This equation is satisfied.
2. **Substituting into the second equation \(3x + y = 0\)**:
\[
3(-2) + 6 = -6 + 6 = 0
\]
This equation is also satisfied.
Since both equations are satisfied by the coordinates \((-2, 6)\), we conclude that \((-2, 6)\) is indeed a solution to the system of equations.
Therefore, the correct response is:
**Yes, because the graphs intersect at (−2, 6).**