# Find the value of 2 terms in the simultaneous equation

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• Oct 25th 2009, 02:32 AM
zorro
Find the value of 2 terms in the simultaneous equation
Question : For what values of $\lambda$ and $\mu$ , the simultaneous equations

x + y + z = 6
x + 2y + 3z = 10
x + 2y + $\lambda$z = $\mu$
• Oct 25th 2009, 02:46 AM
Mush
Quote:

Originally Posted by zorro
Question : For what values of $\lambda$ and $\mu$ , the simultaneous equations

x + y + z = 6
x + 2y + 3z = 10
x + 2y + $\lambda$z = $\mu$

Note that the first two terms of the last two equations are identical. We can rewrite these equations as:

$x + 2y = 10 - 3z$

$x + 2y = \mu - \lambda z$

So we can conclude that $10 - 3z = \mu -\lambda z$.

You can solve for lambda and mu by comparing coefficients of $z^1 \, \, \text{and} z^0$ on each side of this equation.
• Oct 31st 2009, 09:56 PM
zorro
Quote:

Originally Posted by Mush
Note that the first two terms of the last two equations are identical. We can rewrite these equations as:

$x + 2y = 10 - 3z$

$x + 2y = \mu - \lambda z$

So we can conclude that $10 - 3z = \mu -\lambda z$.

You can solve for lambda and mu by comparing coefficients of $z^1 \, \, \text{and} z^0$ on each side of this equation.

But may i know what do u mean by $z^0$ and $z^1$ in the equation
• Oct 31st 2009, 10:29 PM
harbottle
$z^1=z;\quad z^0=1$
• Nov 1st 2009, 12:44 AM
zorro
I am still unable to understand
Quote:

Originally Posted by harbottle
$z^1=z;\quad z^0=1$

But how did u get $z^0 = 1$ $z^1 = z$
Could u please elaborate on that
• Nov 1st 2009, 12:50 AM
mr fantastic
Quote:

Originally Posted by zorro
But how did u get $z^0$ $z^1$
Could u please elaborate on that

Forget the $z^0$ $z^1$ business.

If $10 - 3z = \mu -\lambda z$ for all values of z then it should be quite plain that you need to equate the constant term on each side of the equation and you need to equate the coefficient of z on each side of the equation.
• Nov 1st 2009, 01:09 AM
zorro
Quote:

Originally Posted by mr fantastic
Forget the $z^0$ $z^1$ business.

If $10 - 3z = \mu -\lambda z$ for all values of z then it should be quite plain that you need to equate the constant term on each side of the equation and you need to equate the coefficient of z on each side of the equation.

what do u mean by equating the constant on each side of the equation?
Please could u show me the steps
• Nov 1st 2009, 01:40 AM
mr fantastic
Quote:

Originally Posted by zorro
what do u mean by equating the constant on each side of the equation?
Please could u show me the steps

I will not.

Are you honestly saying that you do not know what the constant term is in $10 - 3z$ and $\mu - \lambda z$? If that's the case then sorry but there's nothing educational to be gained by someone writing a solution for you to simply copy.

The cold hard fact (based on this thead and others) is that you need to go back and thoroughly revise basic material (such as polynomials) because the questions you are asking (and no doubt other questions you have yet to meet or ask) assume you are competent with that material.

• Nov 1st 2009, 01:46 AM
zorro
Quote:

Originally Posted by mr fantastic
I will not.

Are you honestly saying that you do not know what the constant term is in $10 - 3z$ and $\mu - \lambda z$? If that's the case then sorry but there's nothing educational to be gained by someone writing a solution for you to simply copy.

The cold hard fact (based on this thead and others) is that you need to go back and thoroughly revise basic material (such as polynomials) because the questions you are asking (and no doubt other questions you have yet to meet or ask) assume you are competent with that material.

You didnt understand my question . I need to know what to put in the values of mu and lambda
• Nov 1st 2009, 01:50 AM
mr fantastic
Quote:

Originally Posted by zorro
You didnt understand my question . I need to know what to put in the values of mu and lambda

You have been told how to get the values of $\mu$ and $\lambda$. Review my replies and then show your work if you still need help.
• Nov 1st 2009, 02:08 AM
zorro
Quote:

Originally Posted by mr fantastic
Forget the $z^0$ $z^1$ business.

If $10 - 3z = \mu -\lambda z$ for all values of z then it should be quite plain that you need to equate the constant term on each side of the equation and you need to equate the coefficient of z on each side of the equation.

In this u have quoted to equate the coefficient of z on each side of the equation
and here the coefficient of z would be 3 and lambda ...is that correct
If correct then which equation should this coefficient should be equated
• Nov 1st 2009, 02:14 AM
mr fantastic
Quote:

Originally Posted by zorro
In this u have quoted to equate the coefficient of z on each side of the equation
and here the coefficient of z would be 3 and lambda ...is that correct
If correct then which equation should this coefficient should be equated

On the left hand side the coefficient of z is -3. On the right hand side the coefficient of z is $-\lambda$. So $-3 = -\lambda \Rightarrow \lambda = 3$.

Your job is to use similar reasoning with the constant terms.
• Nov 1st 2009, 02:40 AM
zorro
Quote:

Originally Posted by mr fantastic
On the left hand side the coefficient of z is -3. On the right hand side the coefficient of z is $-\lambda$. So $-3 = -\lambda \Rightarrow \lambda = 3$.

Your job is to use similar reasoning with the constant terms.

So the value of lambda = 3 and mu = 10

is that correct ,then what is the use of the other equations in the question ?
• Nov 1st 2009, 03:19 AM
Raoh
(Happy)yes,it is correct , $\lambda =3,\mu =10$.
• Nov 1st 2009, 03:40 AM
mr fantastic
Quote:

Originally Posted by Raoh
(Happy)yes,it is correct , $\lambda =3,\mu =10$.

These are the values for the system to have infinite solutions. But having reviewed the original post, I find that that the OP hasn't said what's meant to be happening with the system ....

Quote:

Originally Posted by zorro
Question : For what values of $\lambda$ and $\mu$ , the simultaneous equations

x + y + z = 6
x + 2y + 3z = 10
x + 2y + $\lambda$z = $\mu$

This question is incomplete. What is meant to happen with these equations? Do you want:

Infinite solutions? Unique solution? No solution?
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