im stuck with simultaneous equations 3x+5y=26 2x+y=16?

👨🏻‍🏫 學術台數學

[匿名]

2009-03-17 3:21 pm

hey guys, im have a real problem with this, i am doing it but the answers i coming up dont fit, i got x=2 and y = 15.
i never liked simulataneous equations, just never got the hang of it, can anyone help me or show me the right way. thank you in advance. jonathan

更新1:

sorry it should be.....3x+5y=26 and 2x+3y=16

更新2:

thank you for all your hard work, sorry i messed the original question up, the stress of maths is getting to me! thank you all again.

回答 (11)

Engr. Ronald

2009-03-17 3:44 pm

✔ 最佳答案

[3x+5y=26]3 multiply 3 to equation 1
[2x+3y=16]5 multiply 5 toequation 2
--------------------
9x+15y=78
-10x-15y=-80 < change sigs of equation 2 to cancel y
---------------------
-x=-2
x=2 answer//

plug in x=2 to equation 1

3(2)+5y=26
6+5y=26
5y=26-6
5y=20
y=4 answer//

checking

3(2)+5(4)=26
6+20=26
26=26 correct!

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An ESL Learner

2009-03-17 3:50 pm

3x + 5y = 26 (solve by using substitution)
2x + 3y = 16

3x + 5y = 26
3x = 26 - 5y
x = (26 - 5y)/3

2x + 3y = 16
2(26 - 5y)/3 + 3y = 16
(52 - 10y)/3 + 3y = 16
3[(52 - 10y)/3 + 3y] = 3[16]
52 - 10y + 9y = 48
-10y + 9y = 48 - 52
-y = -4
y = -4/-1
y = 4

3x + 5y = 26
3x + 5(4) = 26
3x + 20 = 26
3x = 26 - 20
x = 6/3
x = 2

∴ x = 2 , y = 4

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[匿名]

2016-11-01 6:51 pm

ok i shall answer.. a million >2(3x + 2y = a million) >3(2x + 3y = 2) 2 >6x + 4y =2 >6x + 9y = 6 * do away with x by using <-> 3 > 5y = 4 > y = 4/5 *replace y = 4/5 4 > 3x + 2(4/5) =a million > 3x + 8/5 = a million 5 > 3x = a million- 8/5 > 3x = 3/5 6 > x = 3/5 divide 3 > x = 3/5 * a million/3 > x = 3/15 > x = a million/5 wow sorry for quite long,, i wish its marvelous

👍 0 👎 0

[匿名]

2009-03-17 4:21 pm

I also get the same answer as above,

x=7.71 and y=.571 (of course this is the answer to your original equations not the correct ones)

but if your looking to see how to do it for yourself this site is useful.

http://richardbowles.tripod.com/maths/algebra/simeqn.htm

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[匿名]

2009-03-17 3:48 pm

First you multiply each equation so you can remove a variable.

2[(3x+5y)=26]
-3[2x+3y=16]

Add it up, you get
-6x+6x+10y-9y=52-48
y=4

substitute y in [2x+3y=16], you get x=(16-(3*4))/2=4/2=2
x=2
y=4

checking,
3x+5y=3*2+5*4=6+20=26
2x+3y=2*2+3*4=4+12=16

steps:
1. multiply equations
2. add up equations to isolate single variable
3. solve for first variable
4. substitute into any equation to obtain second variable
5. check solution.

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[匿名]

2009-03-17 3:37 pm

Hi jonathan

you are given two equations and are expected to find value for two unknowns namely x and y.

what you want to do is

multiply one of these equation with a scalar number (say, 1, 2, 3, 4...) such that coefficient of one unknown (either x or y) is same as the another.

So,

multiply 2x + y = 16 by 5 inorder to match the coefficient of y (which is 1) to 5y (which is 5)

10x + 5y = 80

now what you want to do is subtract these two equation so that 5y goes away and you end up with one variable (i.e. x).

So,

10x + 5y = 80
-
3x + 5 y = 26

gives

7x = 54

x = 54/ 7

now plug the value of x in either one of those equation and find the value of y

so plugging into 3x+5y = 26 gives

3 * (54/7) + 5y = 27

5y = 27/7

y = 27/35

Hopefully that gives you the idea on how to solve these problem.

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[匿名]

2009-03-17 3:34 pm

3x + 5y = 26
2x + y = 16

Multiply the second equation by -5

3x + 5y = 26
-10x -5y = -80

Add the equations, the y's cancel out

-7x = -54

so x = 54/7

Now plug x into the first equation

3(54/7) + 5y = 26

Solve for y = 4/7

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[匿名]

2009-03-17 3:32 pm

Eliminate one of x or y first.
You have: 3x+5y = 26, and 2x+y = 16.
From 2nd, y=16-2x. Substitute this in the first one.
3x + 5(16-2x) = 26.
3x-10x+80 = 26
Therefore 7x = 54. So x = 54/7
So y = 16 - 2x = 16 - 108/7 = 4/7.

Answer: x = 54/7, y = 4/7.

NB. There are other ways of solving them.

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[匿名]

2009-03-17 3:32 pm

3x + 5y = 26
2x + y = 16 ==> y = 16 - 2x

3x + 5(16 -2x) =26
3x + 80 -10x = 26
-7x + 54 = 0
54 = 7x
x = 54/7
y = 4/7

👍 0 👎 0

[匿名]

2009-03-17 3:32 pm

3x+5y=26 ..(i)

2x+y=16...(ii)

Multiply (ii) by 5,
10x+5y=80...(iii)

subtract (i) from (iii)
7x=54

x=54/7

substitute in (ii)

y=16 - 2*54/7

y=4/7

Solution Set (x,y):(54/7,4/7)
(Ans)

👍 0 👎 0

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