Question
Complete this assessment to review what you've learned. It will not count toward your grade. 2 of 152 of 15 Items Question Is (7, 3) the solution to the system of these linear equations: 3x+2y=5 and −x+6y=11 ? Why?(1 point) Responses No, because the graphs don’t intersect at (7, 3) . No, because the graphs don’t intersect at left parenthesis 7 comma 3 right parenthesis . Yes, because the graphs don’t intersect at (7, 3) . Yes, because the graphs don’t intersect at left parenthesis 7 comma 3 right parenthesis . Yes, because the graphs intersect at (7, 3) . Yes, because the graphs intersect at left parenthesis 7 comma 3 right parenthesis . No, because the graphs intersect at (7, 3) . No, because the graphs intersect at left parenthesis 7 comma 3 right parenthesis . Remaining Attempts : 3 Skip to navigation
Answers
GPT-4o mini
To determine whether (7, 3) is a solution to the system of equations \(3x + 2y = 5\) and \(-x + 6y = 11\), we can substitute \(x = 7\) and \(y = 3\) into both equations and see if the equations are satisfied.
1. For the first equation, \(3x + 2y = 5\):
\[
3(7) + 2(3) = 21 + 6 = 27
\]
Since \(27 \neq 5\), (7, 3) does not satisfy the first equation.
2. For the second equation, \(-x + 6y = 11\):
\[
-7 + 6(3) = -7 + 18 = 11
\]
This equation is satisfied by (7, 3).
Since (7, 3) does not satisfy the first equation, it is not a solution to the system.
Therefore, the correct response is:
**No, because the graphs don’t intersect at (7, 3).**
1. For the first equation, \(3x + 2y = 5\):
\[
3(7) + 2(3) = 21 + 6 = 27
\]
Since \(27 \neq 5\), (7, 3) does not satisfy the first equation.
2. For the second equation, \(-x + 6y = 11\):
\[
-7 + 6(3) = -7 + 18 = 11
\]
This equation is satisfied by (7, 3).
Since (7, 3) does not satisfy the first equation, it is not a solution to the system.
Therefore, the correct response is:
**No, because the graphs don’t intersect at (7, 3).**