Wednesday, February 29, 2012
when doing a simultaneous equation, how do you know how to plus it or minus it?
eg.
1. x+4y=7
2. 2x-3y=4
do you plus or minus it? Also, which one do you change to make it equal? either x and 2x ( times x by 2 to make them both 2x or 4y by 3 and 3y by 4 to make them both equal 12y)|||Don't do either, that method always confused me. Instead, make one of them x= or y=, then just substitute it into the other. You'll get taught to do that when you use simultaneous equations with x^2 etc in anyway.
So with this one, make the top equation x = 7 - 4y
If x = 7 - 4y, then you can replace all x's with (7 - 4y), so substitute that in to the bottom equation:
2(7 - 4y) - 3y = 4 Now just simplify to find what y equals:
14 - 8y - 3y = 4
14 = 4 + 11y
11y = 11
y = 1
Now you can substitute y into the original equation as normal: x + 4x1 = 7
x + 4 = 7
x = 3
Done! Hope that helped|||The two basic methods are SUBSTITUTION and ELIMINATION, and in either case you gan 'go for' X or Y. Just pick the method that --- based on the specific problem --- seems easiest.
Substitution;
x+4y=7 becomes x=7-4y
and plug that into the other equation to get 2(7-4y)-3y=4
Elimination;
x+4y=7 times 2 first.
2x + 8y = 14
2x - 3y = 4
---------------------- subtract
11 y = 10|||It doesn't matter which eq. you choose.
x+4y=7
2x-3y=4
4x+16y=28
4x-6y=8
I subtract the second from the first.
22y=20
y=10/11
x+4y=7
2x-3y=4
2x-3y=4
x+4y=7
2x-3y=4
2x+8y=14
-11y=-10
y=10/11
I subtract the first from the second.|||X =7-4y鈥︹€?call this鈥?.equation 1 why? because is simpler than to say, x=(3y+4)/2. just change the simplest equation and you will never go wrong.
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