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If in equation a(1)x+b(1)y+c(1)=0 and a(...

If in equation `a_(1)x+b_(1)y+c_(1)=0 and a_(2)x+b_(2)y+c_(2)=0` are such that `(a_(1))/(a_(2))ne(b_(1))/(b_(2))`, then which of the following is true?

A

No solution

B

Infinite solution

C

Unique solution

D

None of these

Text Solution

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The correct Answer is:
C
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For two linear equations a_(1)x + b_(1)y + c_(1)= 0 and a_(2) x+ b_(2)y+ c_(2)= 0 , then condition (a_(1))/(a_(2)) = (b_(1))/(b_(2))= (c_(1))/(c_(2)) is for

If the ordered pair satisfying the equations a_(1)x+b_(1)y+c_(1) and a_(2)x+b_(2)y+c_(2) has 1 as its first coordinate,then which of the following is correct?

If the system of equations a_(1)x+b_(1)y+c_(1),a_(2)x+b_(2)y+c_(2)=0 is inconsistent,(a_(1))/(a_(2))=(b_(1))/(b_(2))!=(c_(1))/(c_(2))

Assertion (A) :Pair of linear equations 9x+3y+12=0 and 18x+6y+24=0 have infinitely many solutions Reason (R ) : Pair of linear equations a_(1)x+b_(1)y+c_(1)=0 and a_(2)x+b_(2)y+c_(2)=0 have infinitely many solutions if (a_(1))/(a_(2))=(b_(1))/(b_(2))=(c_(1))/(c_(2))

Assertion (A) : The lines 2x-5y=7 and 6x-15y=8 are parallel lines. Reason (R ) : Pair of linear equations a_(1)x+b_(1)y+c_(1)=0 and a_(2)x+b_(2)y+c_(2)=0 have infinitely many solutions if (a_(1))/(a_(2))=(b_(1))/(b_(2))=(c_(1))/(c_(2))

MBD -HARYANA BOARD-PAIR OF LINEAR EQUATIONS IN TWO VARIABLES-SHORT ANSWER TYPE QUESTIONS
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