Is (−2, 6)
a solution to the system of these linear equations: x+2y=10
and 3x+y=0
? Why?
Responses
No, because the graphs don’t intersect at (−2, 6)
.
No, because the graphs don’t intersect at (−2, 6)
. - incorrect
No, because the graphs intersect at (−2, 6)
.
No, because the graphs intersect at (−2, 6)
. - no response given
Yes, because the graphs intersect at (−2, 6)
.
Yes, because the graphs intersect at (−2, 6)
. - not selected, this is the correct answer
Yes, because the graphs don’t intersect at (−2, 6)
.
No, because when you substitute x=-2 and y=6 into the two equations, they do not satisfy either equation.
wrong
I apologize for the oversight. The correct response is: Yes, because when you substitute x=-2 and y=6 into the two equations, they satisfy both equations.
how did you get that answer
To check if the point (-2, 6) is a solution to the system of equations x + 2y = 10 and 3x + y = 0, you can substitute x = -2 and y = 6 into both equations and see if they hold true.
1. x + 2y = 10:
-2 + 2(6) = 10
-2 + 12 = 10
10 = 10
2. 3x + y = 0:
3(-2) + 6 = 0
-6 + 6 = 0
0 = 0
Since both equations hold true when x = -2 and y = 6, the point (-2, 6) is indeed a solution to the system of equations.
The senior class at Hartford High School is planning their prom. They’ve narrowed the location down to two choices. The Regal Hotel charges, C
, $500 for the ballroom rental fee and $75 per student, s
, for the meal. The Greenhill Country Club charges, C
, $1,000 for the ballroom rental fee and $65 per student, s
, for the meal. Create a pair of linear equations that represent this real-world problem.
Responses
Regal Hotel: C=75s+1,000
; Greenhill Country Club: C=65s+500
Regal Hotel: cap c is equal to 75 s plus 1 comma 000; Greenhill Country Club: cap c is equal to 65 s plus 500 - incorrect
Regal Hotel: C=500s+75
; Greenhill Country Club: C=1,000s+65
Regal Hotel: cap c is equal to 500 s plus 75; Greenhill Country Club: cap c is equal to 1 comma 000 s plus 65 - no response given
Regal Hotel: C=1,000s+75
; Greenhill Country Club: C=500s+65
Regal Hotel: cap c is equal to 1 comma 000 s plus 75; Greenhill Country Club: cap c is equal to 500 s plus 65 - no response given
Regal Hotel: C=75s+500
; Greenhill Country Club: C=65s+1,000
The correct pair of linear equations that represent this real-world problem are:
Regal Hotel: C = 75s + 500
Greenhill Country Club: C = 65s + 1,000
Therefore, the correct response is: Regal Hotel: C=75s+500; Greenhill Country Club: C=65s+1,000
The Jackson Jammers are giving away bags and caps at their next game. The bags, b
, cost them $10 each, and the caps, c
, cost them $5 each. They plan to give away 2,000 total items and have a budget of $12,500. Write the pair of linear equations that model this situation.
Responses
b+c=2,000
; 5b+10c=12,500
b plus c is equal to 2 comma 000; 5 b plus 10 c is equal to 12 comma 500 - incorrect
b+c=12,500
; 5b+10c=2,000
b plus c is equal to 12 comma 500; 5 b plus 10 c is equal to 2 comma 000 - no response given
b+c=12,500
; 10b+5c=2,000
b plus c is equal to 12 comma 500; 10 b plus 5 c is equal to 2 comma 000 - no response given
b+c=2,000
; 10b+5c=12,500
The correct pair of linear equations that model this situation are:
b + c = 2,000
10b + 5c = 12,500
Therefore, the correct response is: b+c=2,000; 10b+5c=12,500