Question

calculate the values of m and n that satisfy the simultaneous linear equations.

7m-2n=24
3m-4n=26

Answer 1

Isolate one of the variables in a equation then sub it into the other.

Answer 2

elimination or replacement

Answer 3

If you don't want to do it that way, you can also add one equation to the other, or subtract one equation from the other.

It's okay to add or subtract equations. You are adding or subtracting equal amounts to both sides, after all! It's important for the subject called "linear algebra."

You do this to try to lose one of the independent variables. Like,

\(\begin{matrix}2x&+&3y&=&13\\5x&+&6y&=&29\end{matrix}\)

I see that \(3y\) is half of \(6y\). So I subtract the first equation from the second equation to get
\(\begin{matrix}2x&+&3y&=&13\\5x-2x&+&6y-3y&=&29-13\end{matrix}\)


\(\begin{matrix}2x&+&3y&=&13\\3x&+&3y&=&16\end{matrix}\)

And once more, so that what was \(6y\) is totally gone,
\(\begin{matrix}2x&+&3y&=&13\\3x-2x&+&3y-3y&=&16-13\end{matrix}\)


\(\begin{matrix}2x&+&3y&=&13\\x&+&0&=&3\end{matrix}\)
Oh, look! \(x=3\)! And now you can substitute it into the top equation and solve for \(y\).

Answer 4

That problem is purposely similar to yours, in case you want to use that technique!

Answer 5

yes but not in my exam.....because i just learn to use elimination or replacement

Answer 6

What I did sounds like elimination, and what @iambatman did looks like replacement (substitution). But I'm not sure.

Answer 7

TQ

Answer 8

Either way should work.

Answer 9

Yup!

Answer 10

TQ?

Answer 11

can you write the answer

Answer 12

I won't give the answer.

Answer 13

other question I get the answer...only this I did not get

Answer 14

Well, give it a second try! :)

Answer 15

7m-2n=24
3m-4n=26

14m-4n=48
3m -4n=26
17m =74

like this

Answer 16

Well, you add \(14m+3m\) to get \(17m\).
\(48+26=74\).

But \(-4n+(-4n)=-4n-4n=...\)
So instead of adding...

Answer 17

I have to go. You just chose the wrong operation. Take care!

Answer 18

that place I wrong

Answer 19

Right. You cannot eliminate the \(n\) terms by addition. So....

Good luck!