Solving Simultaneous equations

Good afternoon my dear friends, I have been giving you definitions for various concept of mathematics. We worked on many problems related to them also. There are many online sites which have algebra practice test, look for such sites and check out the problems in it and try working on them. The subject which has been chosen today is Solving simultaneous equation. I have solved a few of the problems which will help you understand the concept easily.

Look for the problems below.

Problem 1 : Solve 3x – y = 23, 4x + 3y = 48

Solution :

The given equations are :

3x – y = 23 ….(i)

4x +3y = 48 …(ii)

From (i), we get : 3x – y = 23

→ y = 3x – 23 …(iii)

Substituting y = 3x – 23 in (ii), we get : 4x + 3(3x – 23) = 48

= 4x + 9x – 69 = 48

= 13x = 48+ 69

= 13x = 117

= x = 9

Substituting x = 9 in (iii), we get y = 3 × 9 – 23 = 27 – 23 = 4

Hence, x = 9 – 23 = 27 – 23 = 4

Problem 2 : Solve 3x +2y = 2xyi, 6x + 2y = 3xy, where x ≠ 0 and y ≠ 0

Solution :

The given equations are

3x + 2y = 2xy ….(i)

6x + 2y = 3xy …(ii)

On dividing each equation by xy, we get :

3/y + 2/x = 2 …(iii)

6/y + 2/x = 3 …(iv)

Putting 1/x = u and 1/y = v, we get

3v + 2u = 2 …(v)

6v + 2u = 3 . ..(vi)

On subtracting (vi) from (v), we get –3v = – 1 → v = 1/3

Substituting v = 1/3 in (v), we get 3 × 1/3 + 2u = 2 → 1 + 2u = 2 → 2u = 1 → u = 1/2

Now, u = 1/2 →1/x = 1/2 → x = 2

And v = 1/3 → 1/y = 1/3 → y = 3

Hence, x = 2 and y = 3 is the solution of the given equations

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