Answer:
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 !
