Some help with Algebra
January 26th, 2020
http://www.google.com?t=16170191&highlight=
Now I need some help with Algebra.
Please note that this is NOT homework, I’m just trying to learn Algebra.
Here is the equation:
y=2-x-3
I can do these:
-4+y=-2 Without a problem, but when I need to find X and Y it becomes a bit too hard for me, I bet it’s not that hard, but I’ve got no clue to solve it.
Thanks Please remember that ALL links must be coded, including, but not limited to, e-mail addresses, passwords, and internal links. Coded for you this time.
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Usually to solve x and y in one equation, you’ll have 2 equations to work from. Using Simultaneous equations.
Example, you have 2 equations
x+2y= -4, —– (Label as equation 1)
2x+y= 1. —– (Label as equation 2)
From Eq 1 x = -4 -2y ( bring around y ) Substitute this x equation to equation 2
Eq 2
2x +y =1
2( -4-2y ) +y =1
-8-4y +y =1
-3y = 9
y = -3 (answer for y)
Substitute this to any of the equations to find x
You’ll need practice and there are more methods to do it. This is called substitution.
Check out this link http://www.wikihow.com/Solve-Simultaneous-Equations-Using-Substitution-Method
If you have 2 unknown variables, you need 2 equations to find their values (ldo). If you only have one equation, the only thing you can do is assign certain (random) values to one variable (which is agreed to be called independent) then solve and you can find the other variable (which is called dependent as it’s values depend on the values of the independent variable). This is called a function:
http://en.wikipedia.org/wiki/Function_(mathematics)
Ok I’m back again with 2 new equations:
#1: 3x+2=4x-5
What is the “best” way to get x? Most of the times I’m just guessing and guessing.
#2: 4x+21/2=2+3x
#3: 3/2x=1/2x+10
How do I deal with fractions in these kind of equations?
i can do #1.
put all the X’s on one side of the equation and the numbers on the other.
+3x +2 = 4x -5 becomes
+3x -4x = -5 -2
-x = -7
x=7
i can do #1.
put all the X's on one side of the equation and the numbers on the other.
+3x +2 = 4x -5 becomes
+3x -4x = -5 -2
-x = -7
x=7
I see that’s really easy, thanks.
Anyone got tips for #2 and #3?
---------------------------------------------------------------------------------------
#2
do u mean this-> 4x + (21/2) = 2 + 3x
or this -> (4x + 21)/2 = 2 + 3x {please use brackets to make the divider more clear)
================================================
4x + (21/2) = 2 + 3x
=> 4x - 3x + (21/2) = 2 + 3x -3x [ reasoning=> if 45=45, then 45-n=45-n ]
=> x + (21/2) - (21/2) = 2 - (21/2) [ reasoning=> ^^ ]
4 21 => x = ___ - ____ [ reasoning=> 4/2 = 2 ]
2 2
4 - 21
=> x = ________
2
-17 => x = _____
2
so, x = -17/2
================================================
(4x + 21)/2 = 2 + 3x
=> 4x + 21 = 2 * (2 + 3x) [ reasoning=> if a/b = c/d, then a*d = c*b, example=> 3/4 = 6/8, 3*8 = 6*4] => 4x + 21 = 4 + 6x
=> 21 - 4 = 6x - 4x
=> 17 = 2x
=> 17/2 = x
so, x = 17/2
---------------------------------------------------------------------------------------
#3
do u mean this-> 3/2x = (1/2x) + 10
or this -> 3/2x = 1/(2x+10) {please use brackets to make the divider more clear)
================================================
3/2x = (1/2x) + 10
=> (3/2x) - (1/2x) = 10
3 - 1
=> _______ = 10
2x
2
=> ___ = 10
2x
1
=> ___ = 10
x
=> x = 1/10 [ reasoning=> if a/b = c/d, then a/c = b/d, example=> 3/4 = 6/8, 3/6 = 4/8]
so x = 1/10
================================================
3/2x = 1/(2x+10)
=> 3 * (2x+10) = 2x * 1 [ reasoning=> if a/b = c/d, then a*d = c*b, example=> 3/4 = 6/8, 3*8 = 6*4]
=> 6x + 30 = 2x
=> 6x - 2x = -30
=> 4x = -30
=> 2x = -15
=> x = -15/2
so x = -15/2
---------------------------------------------------------------------------------------
#2
do u mean this-> 4x + (21/2) = 2 + 3x
or this -> (4x + 21)/2 = 2 + 3x {please use brackets to make the divider more clear)
================================================
4x + (21/2) = 2 + 3x
=> 4x - 3x + (21/2) = 2 + 3x -3x [ reasoning=> if 45=45, then 45-n=45-n ]
=> x + (21/2) - (21/2) = 2 - (21/2) [ reasoning=> ^^ ]
4 21 => x = ___ - ____ [ reasoning=> 4/2 = 2 ]
2 2
4 - 21
=> x = ________
2
-17 => x = _____
2
so, x = -17/2
================================================
Yeah I know it was annoying to write it like that, but you were right in both equations, the first solution/assumption was the correct one.
I do get #3, because the numerator (if I’m correct) is the same makes it a lot easier, but what for example if one of the 2x was 2y for example?
Ok back to #2
I got it all until:
=> x + (21/2) - (21/2) = 2 - (21/2) [ reasoning=> ^^ ] I don’t understand how you got to the (4/2).
I could never understand Algebra or Geometry and neither ever did me any good, after I began working – so I’m still none the wiser on how to do whatever they do or why.
That said, I am sure there are software programs available which can help you with Algebra and Geometry equations, which you can download off the internet.
Question in Google and see where that takes you – perhaps with a guided PC result, you can self teach yourself how to learn Algebra.
@OP: He just converted 2 to 4/2 ( 2 = 4/2 )
@OP: He just converted 2 to 4/2 ( 2 = 4/2 )Aaah I see.
I could never understand Algebra or Geometry and neither ever did me any good, after I began working - so I'm still none the wiser on how to do whatever they do or why.
That said, I am sure there are software programs available which can help you with Algebra and Geometry equations, which you can download off the internet.
Question in Google and see where that takes you - perhaps with a guided PC result, you can self teach yourself how to learn Algebra.
Yes there is plenty of software available that solves the equations for you, but you don’t learn anything out of it, that’s the whole problem.
Well that was a quick refresher course for me after about 50 years !
And it’s kinda good to see that sort of thing hasn’t really changed since I was in High School.
No calculators allowed then though…Cos they hadn’t been invented !
And Apples were strictly for the teacher wanting to understand the theory and practice is good..
As is all you guys helping him out..
It shows how versatile and helpful a Helpdesk we have.
to solve several variables(x,y,z..) u need several/atleast same numbers of equations(most of the times).
means for 3 variables u need atleast 3 equations.
the working process or the thought process- solving several variable is->
# labeling the equations
## by multiplying the whole equations, changing the numerical value of certain variable/variables in certain equation/equations and make it similar to the other equation�s same variable
### then fixate the equations with other variable/s by cutting off the same, changed variable/s.
doing the process # & ## again, in case of more variables, until finding the answers.
===========================================================
like in the beginning �� try to show. He just used a variation of what I just say
x+2y= -4, ----- (Label as equation 1) 2x+y= 1. ----- (Label as equation 2) From Eq 1 x = -4 -2y (bring around y) Substitute this x equation to equation 2 Eq 2 2x +y =1 2( -4-2y ) +y =1 -8-4y +y =1 -3y = 9 y = -3 (answer for y)===========================================================
#
x+2y= -4 <——————- (Labeling as equation I)
2x+y= 1 <——————- (Labeling as equation II)
[for labeling we usually use roman number to avoid confusion with the numbers from the equation]
##
Multiply the equation (II) by 2
2 * (eq II) ->
2 * (2x+y) = 2 *1 [ reasoning=> if 45=45, then 45*n=45*n ] => 4x + 2y = 2 <——————- (Labeling as equation III)
###
Now substract/minus the eq (III) from eq (I)
(eq I) � (eq III) ->
x + 2y – (4x + 2y) = -4-2
=> x – 4x +2y � 2y = -6
=> -3x =-6
=> 3x = 6 [ multiply the both sides with (-1), reasoning=> if 45=45, then 45*n=45*n ]
=> x = 6/3 = 2
{{{{ After practice, to save time we usually escape the ## & ### processes like this->
(eq I) � 2*(eq II) [ substracting eq(II) from eq(I) ] }}}}
Now apply the x �s value in any eq to get the answer of other variable->
If I apply x=2 in eq (II) ->
2*2+y= 1
=> 4 + y = 1
=> y + 4 � 4 = 1 � 4 [ reasoning=> if 45=45, then 45-n=45-n ]
=> y = 1 – 4 [ ^^ usually we skip that line with reasoning like-> when a character change sides of the (=) �equal to� sign, they change their attributes, what I mean is when u change the sides(left & right), numbers� front signs get plus(+) to minus(-) & minus(-) to plus(+) ] {{ English is not my primary language, and I also forgot most of the native terms of mathematics, let alone I don�t even know the English terms of the mathematics, now or then. So u have to excuse me when using the wrong terms }}
So, y = -3
===========================================================
U say-
because the numerator (if I'm correct) is the same makes it a lot easier, but what for example if one of the 2x was 2y for example?[numerator/dividend is the upper-part, the number that will be divided, denominator/divisor is the lower-part, the number that will divide]
So u means-
1) 3/2x = (1/2y) + 10
2) 3/2y = (1/2x) + 10
3) 3/2x = 1/(2y+10)
4) 3/2y = 1/(2x+10)
===========================================================
I need atleast 2 eq. but here I�ll show u what can we do with 1 eq with 2 variables. Only for the (1) & (3) ===========================================================
1) 3/2x = (1/2y) + 10
3 1
=> ______ = ___ + 10
2x 2y
3 1
=> ______ - ___ = 10 [ changing the sides of the character (1/2y) ]
2x 2y
y*3 x*1
=> ______ - ______ = 10 [ reasoning> a/b = (n*a)/(n*b) ]
y*2x x*2y
[[ u probably already know, when adding/substracting 2 or more fractions, we try to make the denominators/divisors of those fractions similar. means when we try to add 1/2 with 1/3, to make denominators(2,3) similar, we change them to 3/6 & 2/6 { with the reasoning> a/b = (n*a)/(n*b) }. for turning larger denominators (like when adding 2/45 & 7/27), there's some tricks, if u dont know ask here, i'll try to tell u(i remember some terms that are hard to translate). ]]
3y x
=> ______ - _____ = 10
2xy 2xy
3y - x
=> ________ = 10
2xy
=> 3y - x = 10*2xy
=> 3y - x = 20xy
=> 0 = 20xy - 3y + x [ changing the sides of the character 3y & x ]
so, x - 3y + 20xy = 0 [ for confusion, here i dont change the sides but turn the whole eq�s sides left to right while arranging the character as I like]
as I remember when we have equation like this ( ax � bxy � cy = 0 ), there�s 2 way to solve the problem { there could be more }
1st one has something to do with �functions & sets� (forgot the detail) {as �Jack_Torrance� say in the 2nd post}
The main idea is it has equations and some rules about the variable/s.
Suppose, with the equation x – 3y + 20xy = 0 , the rules are y>3 but y<6, the question would be, what are the value of x. more is ib the end of this post
2nd one is like- basic one variable equations->
x^2 � (a�b)x � ba = 0 [ �^� means or pronounce as �to the power�, as here the power is 2, u could say �x square� ]
=> x^2 � ax � bx � ba = 0
=> x(x � a) � b(x � a) = 0
=> (x + a)*(x + b) = 0
So either x + a = 0 or x + b = 0 [reasoning-> when the result of multiplication of 2 number is �0�, then atleast one of them must be �0�]
Example>>
x^2 + 3x + 2 = 0
=> x*x + 2x + 1x + 2 = 0 [reasoning> x*x*x=x^3, x*x=x^2, if x is multiplied by x, n times, then it�ll be x^n]
=> x (x + 2) + 1 (x + 2) = 0 [when we go, x*x + 2x = x (x + 2), we say- �we�re keeping x as common�]
=> (x + 2)( x + 1) = 0 [ keeping (x + 2) as common ]
So either x + 2 = 0 , or x + 1 = 0
If x + 2 = 0
then x = -2
or if x + 1 = 0
then x = -1
so, x = -2 or -1
but this way doesn�t fit for our equation. If we have (not only, there�re various ways) 2xy instead of 20xy, it would fit this kind of equations.
===========================================================
(3) 3/2x = 1/(2y+10)
=> 3*(2y+10) = 1*2x
=> 6y + 30 = 2x
=> 2*(3y+15) = 2*x
=> 3y + 15 = x
=> x � 3y -15 = 0
This equation only fit the first criteria I mention earlier.
In this kind of cases, u put the �variable without rule� or �independent variable� in only one side like->
———————-
From (1)->
x – 3y + 20xy = 0
=> x(1 + 20y) = -3y
=> x = -3y/(1 + 20y)
———————-
From (3)->
x � 3y -15 = 0
=> x = 3y + 15
———————-
Then just apply the possible values of the �variable with rules�, while maintaining the rules, and have the values of �independent variable� in a set.
If y>3 and y<6 then y is a N, [capital N used for positive complete or full numbers, not fractions, not negative, so N=1,2,3,4�]
Then y would be 4, 5
Then x would be->
for (1)-> -4/27, -5/27
For (3)-> 27, 30