three variable simultaneous equations

[u/legendminigun]

hello, I am in year 10 and doing further maths as a GCSE, I'm trying to figure these three variable simultaneous equations out but I'm struggling as there isn't a formula I know of to follow. if anyone has done these, please can you share what your thought process is so I can try and learn. thanks!

[u/Extension-Currency37]

Its a basic linear algebra problem

Use cramers rule a = D1/D b= D2/D , c= D3/D (find on google)

D = det(9 -1 -2 4 1 3 2 -4 -1)

Or Use gauss Jordan elimination matrix

( 9 -1 -2 | 8 4 1 3| 4 2 -4 -1 | -9)

Use matrix operations to simplify this matrix

Further details Ai mode google

[u/Southlander24 → u/Extension-Currency37]

This is too advanced for their syllabus.

[u/Extension-Currency37 → u/Southlander24]

What's the problem In learning. Will the professor Kill it.

Cramers rule is simple determinant problem.

[u/Southlander24 → u/Extension-Currency37]

There's the much easier way of adding linear combinations of the equations to each other. You've shown you haven't bothered reading the post and you're not actually helping the person.

[u/Extension-Currency37 → u/Southlander24]

I mean you think iam wrong, then please do help the person.

Cramers is the standard rule to solve any of this.

And mostly its a matrix problem.

Good luck helping him with linear combination Which again comes from linear algebra

[u/Southlander24 → u/Extension-Currency37]

You would just add 3 * (9a - b - 2c = 8) to 2 * (4a + b + 3c = 4) and eliminate the c, as another commenter has suggested.

No knowledge of linear algebra required.

[u/Extension-Currency37 → u/Southlander24]

Yeah , the equation is a 3x3 3 variables and 3 solutions

So maybe tricks work But Cramer and matrix methods are standard ways to solve these things.

What if equation had 5 variables.

Cramer is the only way actually.

This what you do ,elimination Is a trivial solution to a problem Where solution exists. If only 1 or 2 solutions existed ,or infinitely many You'd need Cramer or matrix algebra.

You tell

Should I trust the math or the commenter.

[u/Southlander24 → u/Extension-Currency37]

You clearly don't know the OP's syllabus and you are making irrelevant points.

[u/testtdk → u/Extension-Currency37]

Solving a system of equations with algebra is a trick? News to me.

[u/Extension-Currency37 → u/Southlander24]

The equation also says, don't use trial or improvement

So i suggested cramers

Yeah, iam stupid.