Question

10. Obtain the condition for two lines to be intersecting, parallel or coincident from the observation table by comparing the values of
a1 ,a2,b1,b2,and c1,c2​

Answer 1

Step-by-step explanation:

The given linear equation are

⇒9x+3y+12=0....eq1

⇒a1=9,b1=3,c1=12

⇒18x+6y+24...eq2

⇒a2=18,b2=6,c2=24

⇒a2a1=189=21

⇒b2b1=63=21

⇒c2c1=2412=21

comparing

⇒a2a1,b2b1,c2c1

⇒a2a1=b2b1=c2c1

Answer 2

• if a1/a2 is not equal to b1/b2, then the pair of equations has intersecting lines ,have a unique solution and are consistent
• if a1/a2 is equal to b1/b2 but not equal to c1/c2 then the lines are parallel, have no solution and dependent consistent
• if a1/a2 is equal to b1/b2 and is equal to c1/c2 then the lines are coincident have infinitely many solutions and are inconsistent.