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can you give me an example of how to work out simultaneous equations. If you could present it step by step and tell me how I work out each step that would be great. If you cant think of an example here is one to work with. Solve the following simultaneous equation 8x-3y=47 11x-12y=41

2006-09-18 08:44:15 · 10 answers · asked by helen y 1 in Science & Mathematics Mathematics

10 answers

solve for x in both equations and then set those equal to each other (having only y variables). solve for y, plug that in one of the original equations. solve for x.

2006-09-18 08:53:55 · answer #1 · answered by ice_purple969 4 · 0 0

8x - 3y = 47
11x - 12y = 41

You can graph the two equations and note the point at which they intersect. This will be approximate unless the x, y values are integers easy to check.

The most obvious way here is to multiply the first equation by 4 and then subtract the second equation from this result.

32x - 12y = 188
11x - 12y = 41
--------------------
21x - 0 = 147
x = 7

Plug this result into either of the original equations to find the corresponding y value.

8(7) - 3y = 47
56 - 3y = 47
- 3y = - 9
y = 3

Check the result using the second equation.

11(7) - 12(3) = 41
77 - 36 = 41
41 = 41

Another approach is to solve one of the equations for either x or y and then plug that expression into the other equation. You will get the same answer.

8x - 3y = 47
-3y = 47 - 8x
y = - (47 - 8x)/3 = (- 47 + 8x)/3 = (8x - 47)/3

11x - 12y = 41
11x - 12(8x - 47)/3 = 41
11x - 4(8x - 47) = 41
11x - 32x + 188 = 41
-21x = - 147
x = 7

You can see why I chose the other method first.

2006-09-18 09:57:43 · answer #2 · answered by Anonymous · 0 0

Given: 8X - 3Y = 47
11X - 12Y = 41

Let: 8X - 3Y = 47 be equation 1
and 11X - 12Y = 41 be equation 2

Now MULTIPLY equation 1 throughout by 4;
Therefore: 32X - 12Y = 188 call this equation 3.

Then use the process of ELIMINATION by subtracting equation 2 from equation 3.
Thus: 32X - 12Y = 188... equation 3
11X - 12Y = 41 ... equation 2
Therefore we get:
32X - 11X = 21X
-12Y + 12Y = 0
188 - 41 = 147

We are left with 21X = 147
Solve for X: X = 147/21 = 7
Substitute X = 7 into EITHER equation 1; 2 or 3 to solve for Y.
Eg: Subst. X = 7 into equation 1(looks the simplest (",) )
Then: 8(7) - 3Y = 47
56 - 3Y = 47
Ergo: 3Y = 9
Y = 3.
Q E D

2006-09-18 09:52:51 · answer #3 · answered by Hoosein 2 · 0 0

There are two simple approaches that come to mind: linear combinations of equations and substitution. For your example, the best way to go would be:

given: 8x-3y=47
11x-12y=41

From first equation, 8x-47=3y
multiply this entire equation by 3: 24x-(47*3)=12y
so 24x-131=12y

now plug in 12y into the second equation
11x-(24x-131)=41
-13x+131=41
13x=90
x=90/13

now, since 24x-131=12y, plug in 90/13 for x to solve for y.

2006-09-18 08:55:15 · answer #4 · answered by need help! 3 · 0 0

there are four methods. you can choose the one which appeals to you
1.the most popular ELIMINATION method

here you make the coefficient of the variable you want to eliminate the same in both the equations by suitably multiplyingthe equation/s
8x-3y=47..........(1)
11x-12y=41......(2)
i will eliminate 'y'
(1)*4 32x-12y=188
11x-12y=41
subtracting21x=147
x=7
substituting x=7 in (1)
56-3y=47
-3y=-9 and so y=3
solution set {7,3}

2.the COMPARISON method
here from both equations you find the value of any one variable interms of the other and then compare those values
8x-3y=47
8x=47+3y
x=(47+3y)/8........(1)
11x-12y=41
11x=41+12y
x=(41+12y)/11....(2)
equate(1) & (2)
(47+3y)/8=(41+12y)/11
cross multiplying
517+33y=328+96y
63y=189 y=3
from(1) x=(47+9)/8=7

3.the SUBSTITUTION method
this is somewhat similar to thecomparison method
here you express one variable in terms of the other in one of the equations and substitute it in the other equation
8x-3y=47.............(1)
x=(47+3y)/8
substitute this in the second equation 11(47+3y)/8-12y=41
517+33y-96y=328
-63y=-189
y=3
substituting in x=(47+3y)/8
x=47+9 /8 x=7

4.the FORMULA method

if the equations are a1x+b1y+c1=0
and a2x+b2y+c2=0
x=(b1c2-b2c1)/(a1b2-a2b1) and y=(a2c1-a1c2)/(a1b2-a2b1)
here a1=8,b1=-3,c1=-47,a2=11,b2=-12 and c2=-41
substituting
x=(123-564)/(-96+33)=7
y=(-517+328)/(-96+33)=3

5.the GRAPH method.
you plot these two lines and the point of intersection will give the solution set

2006-09-18 09:35:06 · answer #5 · answered by raj 7 · 0 0

You need to achieve an equation with only one variable and then the solution is simple.

So you need to look at how you can eliminate one of the variables. In your example , if you multiply the first equation by 4 then you get 32x - 12y = 188.

Now you have 12y in both equations so you add or subtract the equations (according to the signs - in this case as the signs are the same subtract one from the other).

This gives you 21x = 147 which is straightforward to solve.

Once you have found the value of x from this equation merely substitute it in one of the original equations to obtain the value of y.

2006-09-18 09:06:34 · answer #6 · answered by tringyokel 6 · 0 0

Multiply the first equation by -4.. gives you
-32x+12y=-188
adding that equation to 11x-12y=41
gives -21x=-147
solving for x gives x=7
take x=7 back into either equation
8(7)-3y=47
gives y=3..

2006-09-18 08:57:40 · answer #7 · answered by ryan.j.fritz@sbcglobal.net 2 · 0 0

8x-3y=47 ---- (1)
11x-12y=41 ---(2)

(1)x4: 32x-12y=188 ---(3)
(3)-(2): 21x = 147
x = 147/21
x = 7

Substitute x = 7 into (1):
8(7) - 3y=47
56 - 3y = 47
56 - 47 = 3y
9 = 3y
y = 3

2006-09-18 16:03:59 · answer #8 · answered by Kemmy 6 · 0 0

ok so: y=6x+2 'a million' y=-x+13 '2' at the start we call each equation, 'a million' and '2'. then you extremely desire to get an analogous fee for each x (or y, it relies upon on the position that's placed) so that you do equation 'a million' x 6. then you create equation '3': y=6x+seventy 8 '3' (to be endured)

2016-11-27 22:36:45 · answer #9 · answered by Anonymous · 0 0

there are 2 ways helen.first u make X or Y subject of formula in any of the 2 equations,then u replace in second equation...second way is to make X be same figure in both equations,but with different signs.(you do it by multiplying the whole equation OR equations) then u nly add or substract..OUF,exhausted,wel,first method is more simple...after u find X dont forget to find Y.me,i always forget..hpe i`ve bin helpful to you.

2006-09-18 09:07:40 · answer #10 · answered by sweetfloss8 2 · 0 0

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