Can anyone explain how to work out this maths SATS question?

[Florabella]

I know there must be a methodology, but can't remember to explain to my daughter his to do it.

7a - 4b = 2 and 2a + 5b = 19
What are the values of a and b?

Thanks!

I would multiply both until you have a set of b's that cancel each other out -

so 7a-4b (x5) = 35a- 20b = 10 and 2a + 5b (x4) = 8a +20b= 76

Add the results together which give 35a + 8a = 86. So 43a=86, so a=2.

7a - 4b = 2 and 2a + 5b = 19

You need to express a in terms of b by isolating it in one equation, and then put that value into the other equation. That will give you a value for b. Then substitute that in either equation to find a.

So, from the first equation,

a = (2 + 4b)/7

So, using the second equation

2 (2 + 4b) /7 + 5b = 19
(4 + 8b + 35b) / 7 = 19
4 + 43b = 133
43b = 129
B = 3

Using the second equation again
2a + 15 = 19
a = (19-15)/2
a = 2

Thank you so much!!

Thats not SATS level is it?
I think there must be an easier way if working it out?

I would do it as Patricia has said.

However simultaneous equations must be top-top y6 so I really wouldn't worry if it is too much for your y6 at the moment.

My y8 and hasn't done them yet (though she is mid/low set).

If you add the A9.....
add the b 5-4 B1.

A9+B1=19+2
A9+B1=21...
Since it would be whole numbers...
If A was 2 2×9= 18
21-18=3
So A would be 2 and B would be 3

Yikes, wouldn't know where to start with simultaneous equations. When my DS first encountered these, we just did trial and error with simple numbers. Just tried it now and came up with the right answer first time, based on straightforward multiplication that y6 would encounter.

7a - 4b = 2. Right, let's try 2 times table for a.
7x2 = 14. So if the answer is 2, 4b must equal 12. Can 12 be divided by 4, yes.
So b=3. Let's try a=2 and b=3 in the other equation. 2x2=4 plus 5x3= 15 , so 4 plus 15 is 19, so this is correct.
Using 2, 3 , 4, 5 times tables in SATS questions like this worked for my DS. No need to complicate things further for 10 and 11 year olds. If they are happy with their multiplication tables, this should see them through

yes mummy but ultimately that would be trial and error:

9a + b = 21
could be solved by
a=0 b=21 or a=1 b=12 or a=2 b=3 or a=3 b= -6 etc

Then you have to plug back in to one of the other equations.

They shouldn't be giving pupils to do things by trial and error without saying 'using trial and error'.

Patricia's method is a good generic method to solve simultaneous equations.

I think it is rubbish and daft and counter productive to get 10/11 year olds to think that the way to solve simultaneous equations by trial and error. All it will do is store up trouble for later years.

That’s not a SATs question? Where did it come from?

Ok I checked bite size....

It's where as Patricia said.

You have to times the b so they are both the same.. they cancel each other out and you add the a ..

Simple really just do long since I did something like that....

It was on one of the SATS practice papers that we got home. I think I may have made her even more confused when I tried to explain it though 🤣

It is confusing because it has "a" and "b. Replace them with pens and pencils. So the price of 7 pens minus 4 pencils is 3£ and the price of 2 pens and 5 pencils is 20£ (I have made the numbers up).
The fact that you cannot add/subtract one from the other easily makes the problem quite hard. Said that, the "easier" version can be done in earlier years, so perhaps the assumption is that some at least will have done the more complex one. I would guess it is a "greater depth" questions, in which case, fair enough.

9a +b = 21

(basically whack it all together, so add up the a's and add up the b's)

Then 9 x what plus what ==21.

Trial and error. You're only adding to 21 to have to be 2 or less for a as 2 lots of 9 are 27 so too much. Substitute it back in.

100% simultaneous equations for high school but if this is on a SATS paper (highly doubt it) they would be expected just to use the algebra they have been taught (basic) to solve it.

Do they acutually have those question in ks2 sats? I don't think they are within primary curriculum... I maybe wrong, but never thought it would be.

If you were going to use trial and error, then you don't need to do anything to do the equations, just pick one and play around.

2a + 5b = 19

So a = 0 ? => b won't be an integer so probably not.
a=1 ? => b not an integer
a=2 => b=3 possibility so 7a -4b = 14-12 = 2 correct! yippee.

But a rubbish expectation in my opinion. Why teach children to do trial and error rather than wait a year or 2 and then teach them properly.

OP if she can't do it then just tell her to miss it out!

Yep, agree with teen. trial and error for this type of question just seems to be waste of time imo, when you can solve it easily using simultaneous equations.

Any idea where they got that practice paper from. It isn't ks 2 SATs level.

If she hasn't been taught it, i'dbe tempted tolerate that question out because I'd be surprised if anything similar came up on the actual test.

To leave not tolerate.

Let her read the bitesized on it....

You have to increase the equations so you have the same number of b.....

So one is plus the other is a minus....

20 + - 20 = 0

So when you add all the a amounts....
And you add the totals...... you just divide the total by the number of a left it gives her the answer.

To the child who can't do this easily now, few months before sats, does that really help? I would rather spend time going over basics and make sure she/he goes over the question so they didn't make any silly mistakes.

DC1 is in Y4 and he's had similar questions so I assume it is covered in KS2. On the other hand I have A level maths and still struggle with equations

DC1 has understood it best with Venezulan's method

white, it maybe covered, but not as a simultaneous equations, but as in trial and error. Which takes time if you don't get it easily. If it is really a question on sats, no point spending ages on it, better spent somewhere else.

I agree with Irvine . Absolutely no point doing this now if the DC doesn't know how to do it - it will be done properly at some point at secondary.

(Also, no way do I think this is in any way 'standard' for y4.).

It isn’t covered in KS2. It’s a KS3 objective.

Not sure there’s any algebra at all, in the year 4 expectations. I din’t Think it’s introduced until year 6.;