Two equations in this system are EQUIVALENT.


So, they actually represent ONE equation and one straight line.


The system has INFINITELY many solutions.


They all can be presented in the form


    y = 2x - 3,


where x can be ANY real number.

y = 2x - 3 ----- eq (i)

y - 2x = - 3 ----- eq (ii)

DON'T solve eq (ii) for y as she suggests because it makes ABSOLUTELY NO SENSE.

I'm sure no one wants to create extra work for her/himself, and if you still choose to do this, it's additional work you're creating for yourself!



Just substitute 2x - 3 for y in eq (ii) to get: 2x - 3 - 2x = - 3

2x - 2x = - 3 + 3

0 = 0 <===== This equation is TRUE! Therefore, an INFINITE NUMBER of solutions exists for this system.

That's it!! 

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!
 


While tutor @MathTherapy provides many good solutions to readers' problems, you sometimes need to ignore his pronouncements that another tutor's method is "nonsense" and his method is the "right" way.


Solving the second equation makes PERFECT sense; and it leads to the answer to the problem much faster than his method.


Performing a single basic algebraic operation on the second equation makes the two equations identical; therefore the two original equations are equivalent, and therefore the answer is that the system has an infinite number of solutions.


Using the first equation to substitute into the second and then working with that new equation is far more work than adding 2x to both sides of the second equation.


Note that it is curious that he states that nobody wants to make more work for himself in solving a problem -- and then he does exactly that....!


 

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