Simultaneous Help Please (1 Viewer)

[Tyfx]

Okay I got this 3u question I need hhelp with

Consider the equations 12x^2 - 4xy + 11y^2 = 64 and 16x^2 - 9xy + 11y^2 = 78

A) By letting y = mx, show that 7m^2 + 12m - 4 = 0
B) Hence or otherwise solve the two equations Simultaneously

I don't get this question can someone explain on how I can get the answer please thanks

 

[Timske]

i think u sub in y=mx into either equations...

 

[nightweaver066]

Such a tedious question.. Sub one of these m values in to either of the equations [ (3) or (4) ] to get the y values corresponding to it. Then do the same to the other m value.

 

[Tyfx]

Cheeeeers man can you help me with this one as well

2x - y - z = 17
x + 3y + 4z = -20
5x - 2y + 3z = 19

 

[math man]

just do 3(eqn1)+(eqn2) and (eqn3)-2(eqn1) to eliminate y and then solve the two new eqns simulatenously to find x and z

 

[nightweaver066]

Cheeeeers man can you help me with this one as well

2x - y - z = 17
x + 3y + 4z = -20
5x - 2y + 3z = 19

Aim to obtain two equations, both that have the same variables.

If you solve for these two variables first, you'll be able to find the third very easily.

 

[Tyfx]

Cheeers bro I just don't get hte (3) - (1) x 2 : x + 5z = -15
8x + 40z = -120 (5)

how do you get that =/

 

[nightweaver066]

I typed "(3) - (1) x 2" because i was lazy lol.

What it means is multiply (1) by 2 first. Then minus it from (3) and you get the result i had.

I multiplied it by 8 for (5).

 

[cutemouse]

Cheeeeers man can you help me with this one as well

2x - y - z = 17
x + 3y + 4z = -20
5x - 2y + 3z = 19

This shouldn't really be asked in the HSC. It's more of a linear algebra topic.

And if you do it by substitution you always have to check your answers.

The matrix method is much nicer and you can tell straight away if there are no solutions to the system of linear equations.

 

[Carrotsticks]

This shouldn't really be asked in the HSC. It's more of a linear algebra topic.

And if you do it by substitution you always have to check your answers.

The matrix method is much nicer and you can tell straight away if there are no solutions to the system of linear equations.

Cramer's Rule ftw?

 

[cutemouse]

Cramer's Rule ftw?

Well, you can use cramer's rule. But sometimes there will be infinite solutions (in the case where you have, say, 3 variables but only 2 equations).

The matrix method I'm talking about is Gaussian elimination and putting the matrix in row echelon form. In that form you can see immediately if there are no solutions, one solution, or infinitely many solutions.

 

[cutemouse]

Cramer's Rule ftw?

Well, you can use cramer's rule. But sometimes there will be infinite solutions (in the case where you have, say, 3 variables but only 2 equations).

The matrix method I'm talking about is Gaussian elimination and putting the matrix in row echelon form. In that form you can see immediately if there are no solutions, one solution, or infinitely many solutions.