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How To Do Substitution??In math class we are doing these substitution questions and I...

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wwjd | Student, Grade 11 | Salutatorian

Posted February 22, 2010 at 7:09 AM via web

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How To Do Substitution??

In math class we are doing these substitution questions and I don't understand how to do them at all. They are all like this:

The sum of two numbers is 8. Three times the first plus four times the second is 29. Find the numbers.

If you could explain how to do it in steps that would really help! Thanks!! :)

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skyler12 | eNotes Newbie

Posted December 6, 2013 at 12:13 AM (Answer #4)

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well you use the key words that the expression says to help you for example

the word sum means addition or the word of means to multiply like that. I put some other words down below to help you a little more

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krishna-agrawala | College Teacher | Valedictorian

Posted February 22, 2010 at 9:01 AM (Answer #1)

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In the type of question there are two variables to be found out - the two numbers. To find value of two numbers using algebraic equation we need a pair of equation. These two equation can be formed by the two conditions given in the example. That is:

  1. The sum of two numbers is 8.
  2. Three times the first plus four times the second is 29.

Let us assume that the two numbers are x and y.

Then, using the first given condition we form the equation:

x + y = 8    ....   (1)

And using the second given condition we form the equation:

3x + 4y = 29   ....   (2)

We can sole these equation for x an y as follows.

Multiplying equation (1) by 3 we get:

3x + 3 y = 24   ... (3)

subtracting equation 3 from equation 2 we get:

3x - 3x + 4y - 3y = 29 -24

Simplifying the above equation we get:

y = 5.

Substituting this value of y in equation (1), that is using the number 5 instead of y, we get:

x + 5 = 8

Therefore x = 8 - 5 = 3

Therefore the two numbers are 3 and 5.

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job518 | College Teacher | (Level 2) Adjunct Educator

Posted February 22, 2010 at 10:04 AM (Answer #2)

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Since these are two pretty simple equations, you could also do the following:

For (1) a + b = 8  and (2) 3a + 4b = 29

solve (1) for either variable (in this case they both have a coefficient of one so both are just as easy). So subtract b from each side and get a = 8 - b.

Now plug in 8 - b  for a in (2). You will get 3 ( 8 - b ) + 4b = 29. Now simplify and solve for b. 

3 ( 8 - b ) + 4b = 24 - 3b + 4b = 24 + b = 29  => subtract 24 from both sides => b = 5

Now you can substitue b=5 in (1) and get a + 5 = 8 => a =3.

This approach is really best when you are given two simple equations without exponents and a lot of dividing. There are so many ways to do substitution that as long as you are doing legitimate math "moves" and being very careful in simplifying, you will get the same answers. Practice really is the best way to learn it. The link below should help a good deal.

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neela | High School Teacher | Valedictorian

Posted February 22, 2010 at 10:09 AM (Answer #3)

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Substitution and elimation are the techniques employed to used while solving two (or more) simultaneous equations with two (or more) unknwons.Once we detrmined the value of a variable, we substitute the value in any one of the equations to detrmine the other unknown.

We assume two unknown numbers x and y.There two conditions given which is obeyed by these numbers:

By first condition the sum of the numbers, x+y =8 .......... (1).

By 2nd condition, 3times first or 3x and 4times the 2nd or 4y add up 3x+4y and this is 29. So the the second codition is:

3x+4y = 29...............(2).

The two given conditone are the reation between two numbers x and y in the form of above 2equations in 2 variables.

Substitution is a technique, by which we reduce the two equations in two variables to one equation in one variable.

We can use from the first equation x+y = 8,  x = 8-y  in the 2nd equation and replace x in 2nd equation by 8-y, as 3(8-y)+4y = 29 and solve for y. You get now 24-3y+4y =29. Or 24+y = 29. Or y =5.

Using this already detrmined value of  y=5 in any of the two equations, x+y=8 or 3x+4y = 29, we get x+5= 8 . Or x = 8-5 =3. Here also, when we determined one of the value of the two variables, we use the technique of substitution of that velue of the varible to find the value of the other variable.

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Wiggin42 | TA , Grade 11 | Valedictorian

Posted March 23, 2014 at 9:15 PM (Answer #5)

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The sum of two numbers is 8. Three times the first plus four times the second is 29. Find the numbers.

First we must parse the sentence and write it algebraically. 

The sum of two numbers is 8:  a + b = 8

Three times the first (3a) plus four times the second (+ 4b) is 29 (=29) so:

3a + 4b = 29. 

a + b = 8 

Given our two equations, we can solve for a and b. In general, you need as many unique equations as you have variables. 

We know a in terms of b: a = 8 - b

Plug this into the second equation: 

3(8-b) + 4b = 29 Solve for b. 

We know b in terms of a: b = 8 - a

Plug into second equation: 

3a + 4(8-a) = 29 Solve for a. 

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