# Math Help - Find the value of 2 terms in the simultaneous equation

1. ## 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 = $\mu$

2. 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.

3. ## Please elaborate on ur solution

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.

Thanks for ur reply
But may i know what do u mean by $z^0$ and $z^1$ in the equation

4. $z^1=z;\quad z^0=1$

5. ## I am still unable to understand

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

6. 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.

7. 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

8. 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.

Then read threads like this one again.

9. 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.

Then read threads like this one again.

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

10. 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.

11. 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

12. 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.

13. 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 ?

14. yes,it is correct , $\lambda =3,\mu =10$.

15. Originally Posted by Raoh
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 ....

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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