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Maths
GCSE

Using the substitution method, solve the following simultaneous equations 2y+3x=14 and 6x-y=8

Equation 1: 2y+3x=14 Equation 2: 6x-y=8 Rearrange Equation 2: y=6x-8 therefore 2y=12x-16 Substituting the rearranged equation 2 into equation 1: 12x-16+3x=14 15x-16=14 15x=30 x=2 Substituting x into...

Answered by Alex W. Maths tutor
3007 Views

Solve the simultaneous equations 3x+y=16, x+y=10

3x+y=16 (equation 1)x+y=10 (equation 2)Solve by elimination, notice that we have two of the same y's so as they have the same sign we subtract to get 2x=6, we rearrange to get x= 3Sub this back int...

Answered by Meera S. Maths tutor
3038 Views

Prove that the square of an odd number is always 1 more than a multiple of 4

We start off by defining what an odd number is. We take a general letter, say the letter n, to represent any number. If we multiple it by 2 we are sure no matter what number we enter as n the answer will...

Answered by Tanmayi M. Maths tutor
2626 Views

Show algebraically that (4n-3)^2 - (2n+5)^2 is always a multiple of n-4

First we expand the brackets by squaring each side(4n-3)2 = (4n-3)(4n-3)= 16n2 - 24n + 9(2n+5)2 = (2n+5)(2n+5)= 4n2 + 20n + 25Remember the expression i...

Answered by Ella B. Maths tutor
2895 Views

Put the following in order of size, smallest first: 8/sqrt3, sqrt6*sqrt2, sqrt48-sqrt27

First part of the question is to recognise that these are surds and we will need to simplify them. Then it is asking to place the values from smallest to highest. In order to simplify the surds we have t...

Answered by Sandeep S. Maths tutor
2936 Views

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