Classify each system of equations as having a single solution, no solution, or infinite solutions.
y=11 − 2x and 4x − y=7
x=12 − 3y and 3x + 9y =24
2x + y=7 and -6x=3y − 21
x + y=15 and 2x − y=15
2x + y= 7 and -4x=2y + 14
x + 4y=6 and 2x=12 − 8y

1) single solution

2) System has no solution

3)System has infinite solutions

4)System has single solution

5)System has no solution

6)System has infinite solutions

Step-by-step explanation:

Given:

1)

y=11 − 2x and 4x − y=7

substituting y=11-2x in 4x-y=7

4x-(11-2x)=7

4x-11+2x=7

6x=7+11

6x=18

x=3

Putting x=3 in y=11-2x

y=11-2(3)

y=11-6

y=5

system has single solution x=3 and y=5

2)

x=12 − 3y and 3x + 9y=24

Substituting x=12-3y in 3x-9y=24

3(12-3y)-9y=24

36-9y-9y=24

12=0

System has no solution

3)

2x + y=7 and -6x=3y − 21

y=7-2x

substituting above in -6x=3y-21

-6x=3(7-2x)-21

-6x=21-6x-21

0=0

x=7-y/2

System has infinite solutions

4)

x + y=15 and 2x − y=15

x=15-y

substituting above in 2x-y=15

2(15-y)-y=15

30-2y-y=15

-3y=-15

y=5

Putting above in x=15-y

x=15-5

x=10

System has single solution x=10 and y=5

5)

2x + y= 7 and -4x=2y + 14

y=7-2x

substituting above in -4x=2y+14

-4x=2(7-2x)+14

-4x=14-4x+14

0=-28

System has no solution

6)

x + 4y=6 and 2x=12 − 8y

x=6-4y

substituting above in 2x=12-8y

2(6-4y)=12-8y

12-8y=12-8y

0=0

x=6-4y

System has infinite solution x=6-4y !

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the lesson to learn here is that you shouldn't worry about points or rank. chances are, no matter how good an answer you may provide, your efforts will go mostly unnoticed unless you focus on the newest/most active questions that get posted.

7

step-by-step explanation:

i'm assuming you need to figure out how many campers go into each tent.

i got the answer by:

24+4=28

28/4=7