Is there a simple way of solving simultaneous equations?

Answer 1

It depends on how complex they are

1/4 of my final year of maths degree was devoted to this so this gives some idea of how large the subject is

Anyways, subsititution is the basic method for very simple equations

what equation ar eyou trying to solve - email me if you want

Answer 2

Remember any EQUATION has to be EQUAL at all times -

Whatever you do to Left Hand Side (LHS) you MUST also do to Right Hand Side (RHS)

Suppose you were asked to solve:


3b + 2c = 46
3c + b = 11

One way of approaching the question

3b + 2c = 46....................Eq 1
3c + b = 11 ....................Eq 2

Rearrange Eq 2
b = 11 - 3c ..........................Eq 3

Substitute for b in Eq 1
3(11 - 3c) + 2c = 46

Expand terms

33 - 9c + 2c = 46

Collect terms and rearrange
-7c = 46 - 33
7c = -13
c = - (13/7)
c = - 1.9
Substitute for c in Eq 2

3 (-13/7) + b = 11

Rearrange and expand

b = 11 + (39/7)
b = 16.6

OR

You could combine Eq 1 & Eq 2 by rearranging and Subtraction

Eq 1 ............. 3b + 2c = 46
Eq 2 .............. b + 3c = 11

Multiply Eq 2 by 3 (Make coefficient of b the same as it is in Eq 1)

Eq 3 ................3b + 9c = 33
Combine both Equations by subtraction to 'remove' term in 'b'
Eq 1 - Eq 3..... -7c = 13
c = - 13/7


Substitute in Eq 2

3 (-13/7) + b = 11

Rearrange

b = 11 + (39/7)

Depending on the figures you start with, if you follow the steps I have shown, you should be able to deal with ANY pair of Linear Simultaneous Equations

Live Maths ------- Love Maths ------- Breathe Maths

Answer 3

nicely first u label them 2x = 3y ........ a million 2y + x = 7......2 sparkling up 2 for x, so: x = -2y + 7 next u substitute x into quantity a million: 2(-2y + 7) = 3y -4y + 14 = 3y -7y = -14 y = 2 now ultimately to sparkling up for x, substitute the fee of y into quantity one: 2x = 3(2) 2x = 6 x = 3 for this reason, the fee of x is 3 and y is two is often written as (3,2) for a graphing co-ordinate word: the guy who commented first is inaccurate. x can not be 6 and y can not be 2 because of the equation as information. if we substitute those values into the 2x = 3y, it would not equivalent one yet another, at the same time with: 2(6) = 3(2) 12 = 6 incorrect!!!!!!

Answer 4

Yes.
By substitution, elimination, or any one of the methods you already know.

If you have a calculator like mine you can solve linear simultaneous equations with 2 or 3 variables.

You could also try matlab.

Answer 5

Consider the following examples:-
Example1
3x + 4y = 18
5x + 2y = 16

3x + 4y = 18
- 10x - 4y = - 32 CAN NOW ADD
- 7 x = - 14
7x = 14
x = 2

3x + 4y = 18
6 + 4y = 18
4y = 12
y = 3
x = 2 , y = 3

Example 2
2x - 4y = 10
3x + 2y = 7

2x - 4y = 10
6x + 4y = 14-------- ADD
8x = 24
x = 3
18 + 4y = 14
4y = - 4
y = - 1
x = 3 , y = - 1

Example 3
4x - 3y = 12
- 2x + 5y = 8

4x - 3y = 12
-4x + 10y = 16----ADD
7y = 28
y = 4
4x - 12 = 12
4x = 24
x = 6
x = 6,y = 4
Hope you can follow these examples.

Answer 6

For two simultaneous equations, each with y and x, convert them into the following type:

ax+by=e
cx+dy=f

and then:

x = (de-bf)/(ad-bc)
y = (af-ce)/(ad-bc)

For more equations and variables (so with z etc.) you can use row and column operations on matrices (if you are familiar with matrices) - try searching on the web, I can't find anything good though.

Answer 7

Assuming you have the same number of equations as you do variables, you can use substitution or elimination. Substitution means solving for one variable and substituting that for the second variable. Elimination means to add, subtract, mutiply, or divide the two equations to get rid of one variable, then inputting that solution in to the equation of one of the variables.

Answer 8

use gauss jordan Method or row reduction method

Answer 9

Yes, do your homework regularly and study hard. That will make them easy.