Question

Hey guys, please help me how to substitute please provide me the substitution method with example.​

Answer 1

For example take a pair of linear equations

2x +6y =0

8x + 16y = 0

Now convert the first equation in terms of x

2x+6y=0

2x= -6y

x=-3y

No substitute the value you got into the second equation

8x+16y=0

8(-3y) + 16y =0

-24y + 16y =0

-8y =0

y=0

Now we got y= 0 substitute this into x=-3y

we get x=0

Usually this will be numbers other than zero but this is just an example.

Answer 2

Answer:

Observe the steps how to solve the system of linear equations by using the substitution method.

(i) Find the value of one variable in terms of the other from one of the given equations.  

(ii) Substitute the value of this variable in the other equation.  

(iii) Solve the equation and get the value of one of the variables.  

(iv) Substitute the value of this variable in any of the equation to get the value of other variable.

Follow the instructions along with the method of solution of the two simultaneous equations given below to find the value of x and y.  

EXAMPLE :

7x – 3y = 31 --------- (i)  

9x – 5y = 41 --------- (ii)  

Step I: From equation (i) 7x – 3y = 31, express y in terms of x  

From equation (i) 7x – 3y = 31, we get;

     – 3y = 31 – 7x

     or, 3y = 7x – 31

     or, 3y/3 = (7x – 31)/3

     Therefore, y = (7x – 31)/3 --------- (iii)

 

Step II: Substitute the value of y obtained from equation (iii) (7x – 31)/3 in equation (ii) 9x – 5y = 41

  Putting the value of y obtained from equation (iii) in equation (ii) we  get;              

9x – 5 × (7x – 31)/3 = 41 --------- (iv)

Step III: Now, solve equation (iv) 9x – 5 × (7x – 31)/3 = 41

Simplifying equation (iv) 9x – 5 × (7x – 31)/3 = 41 we get;

(27x – 35x + 155)/3 = 41

or, 27x – 35x + 155 = 41 × 3

or, 27x – 35x + 155 = 123

or, –8x + 155 = 123

or, –8x + 155 – 155 = 123 – 155

or, –8x = –32

or, 8x/8 = 32/8

Therefore, x = 4

Step IV: Putting the value of x in equation (iii)  

y = (7x – 31)/3, find the value of y

Putting x = 4 in equation (iii), we get;

y = (7 × 4 – 31)/3

or, y = (28 – 31)/3

or, y = –3/3

Therefore, y = –1

Step V: Write down the required solution of the two simultaneous linear equations by using the substitution method

Therefore, x= 4 and y = –1

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