Classification

[zappafan]

Classify the system as consistent or inconsistent, and dependent or independent.

15x - 3y = -18
-5x - y = 6

Thank you!

[ajb]

As homework we cannot just give you the answer. So, what steps have you tried to solve this question? What methods do you know that may help here?

[studiot]

The equations are dependent if

 

one is a multiple of the other

 

That is if there is one number I can multiply one equation through to get the other.

 

What happens if you multiply the second equation by 3?

Can you now solve the system?

[Nicholas Kang]

I learnt this just 2 weeks ago, in my school. One way is the elimination method, that is eliminate one of the coefficients by multiplying it with whole numbers to obtain the same value with another similar unknown, that is what studiot is saying. The second method is the substitution method, that is by rearranging one of the formulae and place the unknown by the LHS. Then, substitute the formula to the second formula and presto! You will find the answer. But you shall remember that the elimination method is only used in linear functions(functions with the power raised to 1) and cannot be used in quadratic and cubic functions. Substitution method can be used in calculations involving all types of functions.

Edited July 21, 2014 by Nicholas Kang

[studiot]

 

Substitution method can be used in calculations involving all types of functions.

 

 

Hi Nicholas

 

If you do more maths, you will find that it is not always so easy.

 

But yes you have detailed two approaches to solutions.

 

Did you also have any thoughts on the actual question?

 

[Nicholas Kang]

Hi Studiot

 

I haven`t learn consistency or dependency yet. but I know independent variables and dependent variables IN a formula.

[studiot]

 

 

I haven`t learn consistency or dependency yet. but I know independent variables and dependent variables IN a formula.

 

 

Consider the two equations

 

x = 3

2x = 6

 

These equations are really one and the same equation, since we can get the second by multiplying the first through by 2.

 

We say they are dependent.

 

Dependent equations may or may not be solvable.

The ones above are since there is one equation and one unknown

 

but

 

x+y=3

2x+2y=6

 

cannot be solved since there are now two unknowns and only one equation.

 

The second is still double the first and still dependent.

 

Now consider

 

x=3

x²= 1

 

These two equations are not consistent since either can be solved, but there is no solution that satisfies both.

[Nicholas Kang]

Thanks. That is a too-simple-maths idea. Sad to say I haven`t learnt it in Malaysia.