Question

Which of the following pair of linear equation has unique solution, no solution or infinitely many solution:
1) 5x +7y +12 = 0 ; 15x + 21y +36 = 0

2) x -3y -7 = 0 ; 3x -9y +16 = 0

3) 6x -3y +10 = 0 ; 2x -y +9 = 0

Answer 1

Answer:

1: many solution

2: no solution

3: unique solution

Answer 2

Step-by-step explanation: 5x+7y+12=0; 15x+21+36=0

a1/a2=5/15=1/3

b1/b2=7/21=1/3

c1/c2=12/36=1/3

since a1/a2=b1/b2=c1/c2 , therefore it has infinitely many solutions

2) x-3y-7=0; 3x-9y+16=0

a1/a2=1/3

b1/b2= -3/-9= 1/3

c1/c2=-7/16

since a1/a2=b1/b2 not equal to c1/c2, therefore it has no solution

3) 6x-3y+10=0; 2x-y+9=0

a1/a2=6/2=3

b1/b2= 3

c1/c2= 10/9

since a1/a2=b1/b2 not equal to c1/c2, therefore it has no solution