Trial and improvement, or simultaneous equation?

[Precious]

As you may realise from my question my maths is not great, there are some question types on past 11plus papers that im beginning to look at with my DS and i am wondering

x+y=39
x-y=7
what is x?
I just do trial and improvement for this style of question, its all I know, but my older children are telling me this is a simultaneous equation and I need to teach My DS son this, which I'll have to learn myself, are they correct?

Similar questions are : if P is 70 bigger than Q and P+Q =110, what is the value of Q?.. Again I used the trial and improvement method?

All advice appreciated, Thank-you.

[no_ball]

make either y the subject of the equation..
x+y=39, therefore..y=39-x (take x to the other side of the equation, it then goes from being +ve to -ve
x-y=7

therefore, replace the y in the second equation with the re-jigged equation from the first..
x-(39-x)=7
x-39+x=7 (opening up the brackets)
2x-39=7
2x=7+39 (39 becomes +ve going to the otherside of the = sign)
2x=46
therefore x=23

cool, that was from 1987!

Hope that is clear as mud...someone else can put it down better I feel!

[tokyonambu]

That works, but it's messy.

x+y=39
x-y=7

Just add the two equations together. The ys cancel out.

(x + x) + (y - y) = (39 + 7)

2x = 46

x = 23

To check your workings, get y out of the first equation (39 - x = 16) and check the second equation is still true (23 - 16 = 7).

Alternatively, for this special case (and to be honest, I'd be surprised if general simultaneous equations are required at 11+, so this special case may be all that's needed), 7 and 39 are separated by 2y (think of it on a number line). So x must be half way between them 7 + 1/2 (39-7).

[no_ball]

That's works too.

I have taught my method for many years and has always come up in 11+ exams.
Your method is for a slightly older child, not 11+ in my opinion.

[no_ball]

Just some advice, always better to explain the steps involved. For example, explain why the two equations should be added together.

[JaneEyre]

Similar questions are : if P is 70 bigger than Q and P+Q =110, what is the value of Q?.. Again I used the trial and improvement method?

I would resolve it this way:
The exercise give these two information:
P = Q + 70
P+ Q = 110

I use the fist equation into the second which becomes:
Q + 70 + Q = 110
so 2Q = 110-70
so 2Q = 40
so Q = 20
therefore P= 110 -20 = 90

good luck

[wombat1]

The most simple way to explain it to 'pre-algebra' students is:

Take the difference between the two numbers away from the total of the two numbers:
39 - 7 = 32

Then halve this answer:
32 / 2 = 16

This will give the smaller of the two numbers: 16

The larger number is just found by adding 16 and 7: 23

x = 23, y = 16

No algebra involved!

[no_ball]

That's not to say algebra is not needed for some of the entrance exams