Question

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

Answer 1

I hope this helps..!

Answer 2

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

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 !