allegansveritatem
Full Member
- Joined
- Jan 10, 2018
- Messages
- 962
Today I was working on a problem. There was a system of 2 equations that had to be solved using substitution. I had done many of these and this system looked pretty simple.
4x+y=5
7x+3y=10
I took y=5-4x and did this:
4x+5-4x=5
and got the true statement:
5=5.
Not being satisfied with this I plugged 5-4x for y into the second equation and got:
7x+3(5-4x)=10
5x+15=10
x=1
To make a long story short I found that the solution to this system was (1,1) when I put the substitute derived from the first equation into the other equation. But when I tried putting the substitute back into the equation it had been developed from....things went strange.
Of course I went back and studied the chapter again and found that you have to use both equations to get this to work. One equation provides the substitute for the other. How funny I missed that and only now after having done this operation 50 times do I learn it. I guess I was just going by rote and luck before.
But, I would like to ask this: Why doesn't the substitute work on both equations? Seems like it should. I mean, y is y whether it is in one equaton or the other, no?
4x+y=5
7x+3y=10
I took y=5-4x and did this:
4x+5-4x=5
and got the true statement:
5=5.
Not being satisfied with this I plugged 5-4x for y into the second equation and got:
7x+3(5-4x)=10
5x+15=10
x=1
To make a long story short I found that the solution to this system was (1,1) when I put the substitute derived from the first equation into the other equation. But when I tried putting the substitute back into the equation it had been developed from....things went strange.
Of course I went back and studied the chapter again and found that you have to use both equations to get this to work. One equation provides the substitute for the other. How funny I missed that and only now after having done this operation 50 times do I learn it. I guess I was just going by rote and luck before.
But, I would like to ask this: Why doesn't the substitute work on both equations? Seems like it should. I mean, y is y whether it is in one equaton or the other, no?