Question

${} \large \red{good \: evening} \\ \: \: \: \: friends$
pls answer ⭐⭐⭐⭐⭐⭐⭐⭐What is difference
b/w substitution & elimination
method......
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Answer 1

That's a good question. I am surely be elaborating for you in an understandable way.

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Let us take two linear equations with variables x and y as follows :

x + y = 2 ...(i)
3x - 2y = 1 ...(ii)

In the case of substitution, from equation (i), we will express any of x and y in the form of y or x respectively, and then we will put the value of x or y in equation (ii) in places of x or y. Then we will get value of either x or y in its constant one.

In the case of elimination, we will multiply both the equations (i) and (ii) with arbitrary required constants and make the coefficients of either x or y in both the equations the same. Then we will proceed for subtraction between both the equations.

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Substitution Method :

From (i), x + y = 2
or, x = 2 - y

From (ii), substituting the value of x, we get
3 (2 - y) - 2y = 1
or, 6 - 3y - 2y = 1
or, 5y = 5
or, y = 1

Now, putting y = 1 in (i), we get
x + 1 = 2
or, x = 2 - 1
or, x = 1

Thus the required solution be
x = 1, y = 1

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Elimination Method :

The two equations are
x + y = 2 ...(i)
3x - 2y = 1 ...(ii)

Now, multiplying (i) by 3 and (ii) by (i), we get
3x + 3y = 6
3x - 2y = 1

On subtraction, we get
(3x + 3y) - (3x - 2y) = 6 - 1
or, 3x + 3y - 3x + 2y = 5
or, 5y = 5
or, y = 1

Putting y = 1 in (i), we get
x + 1 = 2
or, x = 2 - 1
or, x = 1

Thus the required solution be
x = 1, y = 1

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I hope that you will find it helpful. :)