Simultaneous equations

There are 55 NRICH Mathematical resources connected to Simultaneous equations
Children at Large
problem
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Children at large

Age
11 to 14
Challenge level
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There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
Always Two
problem
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Always two

Age
14 to 18
Challenge level
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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.

System Speak
problem
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System speak

Age
16 to 18
Challenge level
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Five equations... five unknowns... can you solve the system?
Arithmagons
problem
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Arithmagons

Age
11 to 16
Challenge level
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Can you find the values at the vertices when you know the values on the edges?

Surds
problem
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Surds

Age
14 to 16
Challenge level
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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
Warmsnug Double Glazing
problem
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Warmsnug double glazing

Age
14 to 16
Challenge level
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How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
Which is cheaper?
problem
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Which is cheaper?

Age
14 to 16
Challenge level
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When I park my car in Mathstown, there are two car parks to choose from. Can you help me to decide which one to use?
Intersections
problem
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Intersections

Age
14 to 18
Challenge level
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Change one equation in this pair of simultaneous equations very slightly and there is a big change in the solution. Why?
Which is bigger?
problem
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Which is bigger?

Age
14 to 16
Challenge level
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Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?
Graphs of changing areas
problem

Graphs of changing areas

Age
16 to 18
Challenge level
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Use graphs to gain insights into an area and perimeter problem, or use your knowledge of area and perimeter to gain insights into the graphs...