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Solve simultaneously: 2x + y = 18 and x - y = 6

Make both equal to y:y = 18 - 2xy = x - 6Make both equal to each other:18 - 2x = x - 63x = 24x = 8Substitute x into one of the original equations:x - y = 68 - y = 6y = 2So x = 8 and y = 2

Answered by Tutor406540 D. • Maths tutor

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Prove that the difference between the squares of two consecutive odd numbers is a multiple of 8.

(2n+3)²-(2n+1)²=(4n²+12n+9)-(4n²+4n+1)=8n+8= 8(n+1)Hence a multiple of 8

Answered by Daniel B. • Maths tutor

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

2n+1 will always be an odd number (e.g. if n is equal to 3 the answer would be 7, an odd number) So, we square 2n+1 and write this as (2n+1)² 2n +12n 4n...

Answered by • Maths tutor

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There are 495 coins in a bottle. 1/3 of the coins are £1 coins. 124 of the coins are 50p coins. The rest of the coins are 20p coins. Work out the total value of the 495 coins

495/3 = 165 => £165 worth of £1 coins
124 x 0.5 = 62 => £62 worth of 50p coins
We know the number of coins that are NOT 20p coins. Therefore, we can subt...

Answered by Sim B. • Maths tutor

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