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!