SOLUTION: determine whether each system of linear equations has a) one and only one solution b) infinitely solutions c) no solution -10x+15y=-3 4x-6y=-3

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Question 1106909: determine whether each system of linear equations has a) one and only one solution b) infinitely solutions c) no solution
-10x+15y=-3
4x-6y=-3
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
The slopes are the same and these lines will NOT intersect. y-axis intercepts are not the same for each equation, so parallel; not the same line.

No solution to the system.
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.
determine whether each system of linear equations has a) one and only one solution b) infinitely solutions c) no solution
-10x+15y=-3
4x-6y=-3
~~~~~~~~~~~~~~~~~~ 

-10x + 15y = -3     (1)
  4x -  6y = -3     (2)


Divide the equation (1) by (-5)  (both sides).

Divide the equation (2) by 2  (both sides).  You will get and equivalent system

  2x  - 3y =    (1')

  2x - 3y =     (2')


Left sides of equations (1') and (2') are IDENTICAL, which means that left sides are equal at each values of x and y.

But right sides ARE NOT EQUAL.


It means that the system (1'),(2')  HAS NO SOLUTIONS.


Then the equivalent system (1),(2)  HAS NO SOLUTIONS, too.


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