Expert Answers
ncchemist eNotes educator| Certified Educator

In algebra, substitution is a method you can use to solve a system of equations with more than one variable.  Specifically, you solve one equation for one variable in terms of the other, and then substitute the resulting value back into the other equation.  An example is shown below.

2x - 3y = -2   (1)

4x + y = 24    (2)

We need to solve this for x and y.  To start, we need to solve one of the equations for one variable in terms of another.  Let's solve the second equation (2) for y in terms of x:

4x + y = 24

y = 24 - 4x   (3)

Now we can take this value and substitute it back into the first equation (1).

2x - 3y = -2    Now switch y with 24-2x:

2x - 3(24-2x) = -2

2x - (72 - 12x) = -2

2x - 72 + 12x = -2

14x - 72 = -2

14x = 70

x = 5

So we know that x=5.  Now substitute this value back into equation (3) to solve for y:

y = 24 - 4x   substitute x with 5:

y = 24 - 4(5)

y = 24 - 20 = 4

So the final answer is x=5 and y=4.

marizi eNotes educator| Certified Educator

Substitute is to replace a value or with its equivalent value that can be a number or expression.

 One application is construction of table for ordered paisr (x,y) of a line equation: y = x+3

 Substitute set value of x to solve for y.


 x           x+ 3 = y

-2         (-2)+3 = 1

-1          (-1)+3 = 2

0             (0)+3 = 3

1             (1) + 3 = 4

2              (2) + 3 =5

The ones inside the () are the substituted value in x.

Set of points (x,y):  { (-2,1) ,(-1,2), (0,3), (1,4), (2,5)}

Another example:

14x =2x+ 12x to substitute in 6x^2+14x +4.

   6x^2   +  14x   +4


   6x^2 + 2x +12x +4           

Note:  6x^2   +  14x   +4 =   6x^2   +  14x   +4

zumba96 | Student

Substitution is when you put in a value for x in an equation such as x=2, x+2=__

2+2=4. This is used in algebra and is one of the starting points of math used. You should always label your equations and don't forget to input, and after you input you have your answer. Hope that helps :)            

malkaam | Student

Substitution is a method used to solve simultaneous equations. It's a very simple method all you have to do is follow these simple steps:

  • The first thing you should do is label your equations as i and ii. 
  • After that choose any one equation and isolate any one variable in it in order to solve it.
  • After this input the value of the variable in eq(ii) and solve, this will help you get the value of one variable for example x.
  • Then input the value of x in eq(ii) with which you will obtain the value of y.
  • Therefore you have your solution set. If you want to check that your answers are correct then input the value of both variables in any equation if the answers you get are both equal to one another i.e. LHS=RHS then your answer is correct. 
chrisyhsun | Student

Substitution is a common technique in solving systems of equations. In substitution, you plug in some expression that you know is equivalent to a variable for that variable n a different equation. This is often used to make all the unknowns in an equation into one variable so that the equation can be solved. This is important because one equation can only be used to deduce the value of one variable. Here is an example of substitution:

y = 5x + 2

24 = 2y + 10x

According to this system of equations, we know that the expression "5x + 2" is equivalent to the variable y. As such, we can replace the y in the second equation with this expression. Therefore, the second equation can be rewritten as:

24 = 2(5x + 2) + 10x

Algebra will show that this gives a value of 1 for x. This is why substitution is useful. We managed to narrow down the second equation to only contain one variable which allowed us to solve for the variable (in this case x). Also, we can use this value to find the value of y, the variable we substituted the expression for. Going back, this would not have been possible had we only been given the second equation because the single equation is not enough to solve for two variables.

ssarfraz | Student

Basically the word Substitute means an alternate or in place of another. Simply in algebra, substitution means putting numbers in place of letters or putting numbers as substitute for letters.

For example;

An algebraic equation contain letters like:

x + 2 + 5

If x = 5 then we will be Putting 5 as x's substitute, like this:

5 + 2 + 5 = 12