# How do you solve simultaneous linear equations inequalities? (examples are down in the description). Please help!

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Here, this is a problem that I know the answer to, but I seriously have NO idea on how to solve it! Seriously!ðŸ‘‡ðŸ‘‡ðŸ‘‡

#7x+2y=12#

{

#5x+2y=8#

That's the question and the answer to that is #2,-1# . So palease help! I have one more question like that, too.:

#x+y+z=6#

#x+2y+3z=14#

#x+3y+7z=28#

Whats the answer, procedure, steps. I don't get it! Please help (I know that I probably said that a hundred times by now, but back to the point...)

Here, this is a problem that I know the answer to, but I seriously have NO idea on how to solve it! Seriously!ðŸ‘‡ðŸ‘‡ðŸ‘‡

{

That's the question and the answer to that is

Whats the answer, procedure, steps. I don't get it! Please help (I know that I probably said that a hundred times by now, but back to the point...)

##### 1 Answer

Q1:

Q2:

#### Explanation:

Although you ask for methods of solving simultaneous linear **inequalities** , both you example are linear equalities. So I assume you meant **equalities**.

There are 3 basic methods of solving systems of simultaneous linear equations.

(i) **Substitution** : Isolate one variable in terms of the others and replace in another equation. Continue until all are resolved.

(ii) **Linear manipulation** : Multiply one equation by a constant (could be 1) and add/subtract another equation so as to remove a variable. Continue until all are resolved.

(iii) **Matrix inversion** : Express the coefficients of the variables as matrix

In broad terms, these are increasing in complexity and their use will usually depend on the number of variables in the system.

Q1:

Here we have a simple case with only 2 variables. Both methods (i) and (ii) would be appropriate. However, notice that the coefficient of

[A] - [B}:

From [A} with

Hence, our result:

Q2:

Here we have a 3 variable system. In my opinion, method (ii) is most appropriate here too.

[C] - [A]:

[C - [B]:

From [E] with

From [A] with

Hence, our result: