any maths whizzes around? - simultaneous equations help please

[poopscoop]

5x + 3y = 23
2x - y = 7

Now, we have got the answer x = 4 and y = 1

Please can someone talk me through how we get the answer

thanks!

I think you have to multiply one of them to get the figure to "match"

so

2x - y = 7
6x - 3y = 21 (each bit tripled)

Then add the two together -

5x + 3y = 23
6x - 3y = 21

5x + 6x + 3y - 3y + 23 + 21

The +3y and -3y cancel each other out

5x + 6x = 23 + 21

11x = 44

x=4

Then you put the x=4 back into one of the equations to get y

5x + 3y=23
(5 x 4) + 3y = 23
20 + 3y = 23
3y = 3
y = 1

Make sense?

you need to make both equations read the same for y,
so scale equation 2 up by 3 throughout the equation
This gives you
5x + 3y = 23 and
6x - 3y = 21

When the signs are the same you subtract the second from the first, . In this case signs are same so you add both equations.

this gives
11x + 0y (the ys cancel out) = 44

x = 44/11 = 4

then you can substitute for x in either equation. putting 4 in place of x in equation 1 gives you
20 + 3y = 23

Rearrange this to give
3y = 23-20

3y = 3
Therefore y =1

lol. x posts with you all.

everyone is a maths whizz this morning!

you need to eliminate the x or the y to start with - so rearrange one to make x=... or y=....

and then put that value into the other equation.

I would do it the way AMIS said because although it is more steps the numbers are simpler.

5x + 3y = 23

so 5x = 23 - 3y

and -y = 7 - 2x

Substitute so 5x = 23 -3(-7 + 2x)

= 5x = 23 +21 - 6x

so 11x = 44 so x = 44/11 = 4

Then sub back into 2x - y = 7 and solve for y

8- y = 7 so -y = 7-8 so y = 1

HTH

Feck how slow am I - shouldn't have made a coffee!

Take the second equation 2x - y = 7 and rearrange (assume you're OK with this?) to say y = 2x - 7.

Multiply by 3, to get 3y = 6x - 21.

Replace the 3y in equation 1 with 6x - 21, so you have 5x + 6x - 21 = 23 or 11x - 21 = 23 or 11x = 44 so x = 4.

Now put this in eq.2 (2x-y=7), or 8 - y = 7, so y = 1.

And so many different explanations have probably confused you even more!

Mine was from DH and he is fed up with me for not understanding it...

thanks all, we have been studying the above and it really has helped.

Gosh you lot are so brainy.

No doubt we shall be back when stuck on something else!