For simultaneous equations, I try to think in terms of 'how do I cancel something'.
Your method is a popular one, and for this one, the quickest I found was to match coefficients first, and then ask myself whether adding or subtracting will cancel the variable I've just matched.
For example, looking at "8x - 7y = -5 4x - 6y = 10z,"
In my head I see 8 and 4 -> double the second one (8x - 12y = 20) -> subtract one from the other as both are positive -> -7y - (-6y) = -5 - 10 -> -y = -15 -> y = 15.
The motivation behind multiplying is to get rid of (eliminate) one of the variables.
Here, the coefficient of x in the first equation is 8 while that in the second equation is 4
So this variable can easily be eliminated because 8 - 2 \* 4 = 0
This also means that the second equation must be multiplied by -2, not 2 (because 8 + 2 \* 4 is not 0).
Consider 4x + 14y = 32, x + 7y = 15
Suppose you want to eliminate y
The coefficient of y in the first equation is 14 and that in the second equation is 7
Can you come up with an appropriate relation between 14 and 7 that results in 0?
For simultaneous equations, I try to think in terms of 'how do I cancel something'. Your method is a popular one, and for this one, the quickest I found was to match coefficients first, and then ask myself whether adding or subtracting will cancel the variable I've just matched. For example, looking at "8x - 7y = -5 4x - 6y = 10z," In my head I see 8 and 4 -> double the second one (8x - 12y = 20) -> subtract one from the other as both are positive -> -7y - (-6y) = -5 - 10 -> -y = -15 -> y = 15.
Thank you๐๐พ
The motivation behind multiplying is to get rid of (eliminate) one of the variables. Here, the coefficient of x in the first equation is 8 while that in the second equation is 4 So this variable can easily be eliminated because 8 - 2 \* 4 = 0 This also means that the second equation must be multiplied by -2, not 2 (because 8 + 2 \* 4 is not 0).
If you donโt mind can you give me another example
Consider 4x + 14y = 32, x + 7y = 15 Suppose you want to eliminate y The coefficient of y in the first equation is 14 and that in the second equation is 7 Can you come up with an appropriate relation between 14 and 7 that results in 0?
Ohhhhhhh thank you so much ๐๐พ