Simultaneous equations

There are 55 NRICH Mathematical resources connected to Simultaneous equations

problem

Favourite

Fruity totals

Age

7 to 16

Challenge level

In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?

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Favourite

Multiplication arithmagons

Age

14 to 16

Challenge level

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

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Favourite

Leonardo's problem

Age

14 to 18

Challenge level

A, B & C own a half, a third and a sixth of a coin collection. Each grab some coins, return some, then share equally what they had put back, finishing with their own share. How rich are they?

problem

Favourite

Sweet shop

Age

11 to 14

Challenge level

Five children went into the sweet shop after school. There were choco bars, chews, mini eggs and lollypops, all costing under 50p. Suggest a way in which Nathan could spend all his money.

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Favourite

Quadratic harmony

Age

16 to 18

Challenge level

Find all positive integers a and b for which the two equations: x^2-ax+b = 0 and x^2-bx+a = 0 both have positive integer solutions.

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Favourite

Children at large

Age

11 to 14

Challenge level

There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?

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Favourite

Always two

Age

14 to 18

Challenge level

Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.

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Favourite

System speak

Age

16 to 18

Challenge level

Five equations... five unknowns... can you solve the system?

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Favourite

Arithmagons

Age

11 to 16

Challenge level

Can you find the values at the vertices when you know the values on the edges?

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Favourite

Surds

Age

14 to 16

Challenge level

Find the exact values of x, y and a satisfying the following system of equations: 1/(a+1) = a - 1 x + y = 2a x = ay