System of Equations

[Iceycold12]

Hello, is this true? Say I am given a system of equations, and say 1 equation ends in = 10 and the other ends in = 12, I was told that if the answers A, B, C, or D, are x,y coordinates I can just plug in the x and y values and if both equations are true (equation 1 equals 10 and equation 2 equals 12), the correct answer are the x,y coordinates that made both equations true? It's not a matter of helping with a problem, just want to know if this method is valid.

Thanks.

 

[mmm4444bot]

What you describe sounds like a guess-and-check method. You should ask your instructor whether such methods are valid in your course. Some instructors accept them as valid; others do not. You might get partial credit; you might not.

Personally, I think that it is better to learn the simple methods for solving systems of equations because those methods are what the instructor likes to see. :cool:

 

[Iceycold12]

What you describe sounds like a guess-and-check method. You should ask your instructor whether such methods are valid in your course. Some instructors accept them as valid; others do not. You might get partial credit; you might not.
Personally, I think that it is better to learn the simple methods for solving systems of equations because those methods are what the instructor likes to see.

I do know the other methods, I just found out about this one today and wanted to know if it works.

Post an actual problem. What you posted is highly unclear...

I didn't want to post a problem because the numbers would be made up, but okay here we go.

Say answer A, is (4,3) the equations are:

2x+5y=23
3x+4y=24

As you can see, if we plug in (4,3) into each equation, and solve, they both hold true, since 2(4)+5(3)=23 and 3(4)+4(3)=24. And so the answer is A, is this method correct? I'd obviously only use it for cases that I have answer choices and they are all x,y coordinates.

 

[tkhunny]

Hello, is this true? Say I am given a system of equations, and say 1 equation ends in = 10 and the other ends in = 12, I was told that if the answers A, B, C, or D, are x,y coordinates I can just plug in the x and y values and if both equations are true (equation 1 equals 10 and equation 2 equals 12), the correct answer are the x,y coordinates that made both equations true? It's not a matter of helping with a problem, just want to know if this method is valid.

Thanks.

Rule of Thumb, either thumb: If your instructions use the phrase "just plug in", you should ignore the instructions and run quickly away from your instructor.

Rule of Big Toe: If you know solutions, yes, you can just substitute. If you do not know solutions, such an effort is not nearly so hopeful as a needle in a haystack.

Official Opinion: No, what you have suggested should not be considered a "method" at all, let alone a good method. It's just a shot into the murkiest of glooms.

 

[HallsofIvy]

Without saying whether this is a good test or not, it is certainly true that saying that an (x, y) pair is a solution to a system of equations means that if you replace the "x" and "y" variables in the equations by those numbers, the equations are satisfied.

 

[Iceycold12]

JeffM by you approving that yes it does work were you referring to this?

Say answer A, is (4,3) the equations are:
2x+5y=23
3x+4y=24
As you can see, if we plug in (4,3) into each equation, and solve, they both hold true, since 2(4)+5(3)=23 and 3(4)+4(3)=24. And so the answer is A, is this method correct? I'd obviously only use it for cases that I have answer choices and they are all x,y coordinates.

I posted this afterwards in case you need an example, I think I was unclear in the original post.

And I know this is a messy way of doing it, I just saw it working and wanted to make sure I knew it in case I needed to use it one day. I usually use the substitution method of finding y in one equation, plugging in y to the other equation which gives me x and plugging x into the other equation which results in my (x,y) answer.

edit: Hallsofivy just saw your reply, seems you posted right before this one, okay, thank you for confirming.

 

[HallsofIvy]

Not too many years ago, I had a student who complained bitterly that I was marking his answers wrong just because he was using the method he had learned in highschool rather than the method I was teaching. I tried to explain that I was marking his answers wrong because they did not satisfy the equations. I'm not sure that he grasped the idea that 'solutions' to equations were supposed to "satisfy" the equations. He seemed to think that the solutions to equations were 'whatever you get by using this method'.