Help! I'm stumped on the Year 4 maths homework

[MrsFogi]

and don't want to let on to dd that I don't know how to tackle it. So the question is x+y=67 and x-y=19 what do x and y represent? Can someone explain to me so that I can then pass this off as my own brilliant competence in maths [dies of embarrassment smiley/there is not hope for my children smileys].

Add each side of the two equations...
X+Y+x-y =2x
67+19 = 86

So 2x=86, x=43
Then go back to either of the original equations

X + y = 67
43 + y = 67
Y= 24

Sorry I can't help you but I opened the thread because I'm also stumped by y4 maths homework!! To me the method we need to use four ours is long division but DC is doing some other weird and wonderful method which is getting the wrong answer so they want help! What are we going to do when they get to secondary?!

X=43, y=24.

The total of x and y is 67 and x is 19 more than y.
So 67-19 divided by 2 equals y.
X = y + 19.

How is the actual homework worded? In year four I wonder if they're just wanting the children to experiment with different ways of working it out rather than solving simultaneous equations.

I can explain it I think!

DC is doing some other weird and wonderful method. This I mean!!

In year 4 I wonder if they're looking for a trial and error sort of method rather than algebra. So e.g. try x=25 then 25+y=67 so y= 42, oh no x-y is negative. (Or a brighter child would realise to start with x the bigger number.) Okay, so how about if x=42 and y=25, then x-y=17, that's close, but I need x bigger and y smaller. x=43, y=24 - ahah that works!

taking x+y==67 to be equation I and x-y==19 to be equation II;

you can read off term by term and place the coefficients in a matrix.
to do this, I will say that equation I becomes, and is mathematically equivalent to:

1x1+1x2==67

and do similar for equation II.

Now, reading off values, we define the matrix:

A== [1 1 67
1 -1 19]

Note that the columns of A are vectors that relate to x1 and x2 (formerly y) respectively.

getting this matrix to reduced row echelon form using gaussian elimination (you can google this bit if you like, or just use matlab/other tool), you reach the matrix

A==[1 0 43
0 1 24]

hit post too soon dammit.

As we have the identity matrix in R^2 on the left, we can simply read off the values. line-by-line, we see that;

1 x_1=43

and

1 x_2=24

and you're done!
If you dont get the identity matrix, first double check your row reductions. if you get a whole row equalling zero, then this is fine, 0+0=0, right? it just means you are going to have a free variable, then you would leave it in the answer (and maybe writ it as a vector depending on your choosing). otherwise if 0+0=something not 0, then the set is inconsistent and cant be solved :D

Ha! ha! you want a year 4 pupil to learn Gaussian elimination to solve equations with only two unknowns?

As you're wielding your sledgehammer in August and the problem was posted in March, I fear the nut may already be cracked.

Its a skill for life... best to start learning these things on small systems before you move on to 5+ variables. everything is easier in linear algebra if you know gaussian elimination ;)

Yes, but at the age of 8, it's going to be a while before she moves on to systems of 5+ variables. The maths curriculum is structured to introduce these things at an appropriate time, and you're talking about a technique that she's only likely to encounter if she takes a maths route post-16.

its on the high school/gymnasium curriculums and moldova and germany from UK equivalent year 9... granted, yes year 4 is probably a bit early, but why not have it in its basic form in lower secondary school?

x+y=67 consider as - (1)
x-y=19 consider as - (2)

(1) - (2)
(x+y)-(x-y) = 67-19
x+y-x+y=48
2y = 48
y= 48/2
y=24

Now since y=24 we can find x as below
x+y=67
x+ 24 = 67
x=67-24
x=43

OR you can take

x-y=19
x - 24=19
x=19+24
x=43

So you can see which ever you take the answer is x=43, so its your preference
then
y=24 and
x=43

Hope you got it with the step by step guide

Amy - they probably got it when several people explained it in March! The only person reading this thread is me and the gaussian elimination guy.