thank u to whoever tries this problem!!!

- Thread starter happyfish
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thank u to whoever tries this problem!!!

A system of equations in two variables will have infinitely many solutions if the two equations represent the same line.happyfish said:Susan is thinking of a equation that is in the form Ax + By = C. Giver her any linear equation and she guarantees that her equation and yours will form a system with indefinitely many solutions. What is her equation?

thank u to whoever tries this problem!!!

So,

suppose I give you the equation

3x + 2y = 5

If you multiply both sides of my equation by the same non-zero number, your equation and mine will have the same solutions. That's because of the Multiplication Property of Equality, which says that if two things are equal, then the results of multiplying both of them by the same thing must be equal as well. Suppose you multiply both sides of my equation by -3, and get

-9x - 6y = -15

Any ordered pair (x, y) which satisfies MY equation will satisfy yours also. So, the system of equations consisting of your equation and my equation will have infinitely many solutions.

Now....you can take this idea and write an answer to your question, I hope!

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Are there any restrictions on A, B, and C?happyfish said:Susan is thinking of a equation that is in the form Ax + By = C....What is her equation?

Are we assuming that she is thinking of one specific equation, before you ever state what your equation is?

Thank you.

Eliz.

Are we assuming that she is thinking of one specific equation, before you ever state what your equation is?

Eliz."

I think A, B, and C have to be whole numbers. Yes, we are assuming that she is thinking of one specific equation. Thank you.

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If we are to assume that she has one equation that she says will work for any equation we give her, then, yes, I think you are correct. It's a "trivial" solution, but it would fulfill the requirements.happyfish said:is the answer 0x + 0y = 0?

Eliz.