Simultaneous equations gcse level help

[Polgara2]

Can anyone explain how to do these equations?

Y=x squared + 3
y=3x+7

X squared + y squared = 106
x+y = 14

a squared + b squared = 113
2b - a = 9

dd2 is actually very good at maths but unfortunately has a teacher who doesn't explain things very well and has given them these to do without the backup of their books to back check. she has managed halfnof the worksheet but struggling on these, she says she uses the substitution method

It may as well be written in another language to me I am afraid

Many thanks - I hate not being able to help them

If two things equal the same thing, then they must equal each other.

Therefore x^2 + 3 = 3x + 7

...then get DS to take it from there :)

The second one you substitute x = 14-y

If she can't solve using factoring, she has to use the quadratic formula. Google it if she has never heard of it before.

Following on from above.

If x squared + 3 = 3x + 7
Then x squared - 4 - 3x = 0
Then put into 2 sets of brackets
(x-4)(x+1) = 0
Then either x-4 = 0 so x= 4
Or x+1=0 so x=-1

Hope that helps

Wow that's great, thanks ladies! She is trying them out now.

Ok she is working on the second one and has got to the point where she wants to find the square root of a negative number, which you apparently can't do? I googled a formula but she said it didn't make sense!
Thanks again

You can't square root a negative number: if you have to, you've gone wrong! The formula you found is for beyond A-Level maths.

For 'quadratic' equations (with squares) she needs to factorise, which she should have done if these questions are being set (otherwise go on youtube for a detailed explanation).

Check for negatives and double negatives (which make positives) as these are often a source of error, though if she isn't getting whole numbers or simple fractions there may be a problem with the question.

Ok right, well she said she is using the quadratic formula and son is going off to go over her working out!

Apparently, they have only done one lesson of substituting to solve simultaneous equations so far and then been given the worksheet. As I said, unfortunately her teacher is not very good which doesn't help. Apparently she often writes things wrong on the board and the kids point it out!

Oopsy , that should have read so she is going over her working out - I don't have a son lol! I can't type on my iPad obviously