Quadratic simultaneous equations

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Simon Thomas

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Simon Thomas 5 years ago

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Simon Thomas 5 years ago

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Question statement

Solve the simultaneous equations:

$x+2y=\var{x+2y}$

$x^2+y^2=\var{x^2+y^2}$

Give any introductory information the student needs.

			Name	Type	Generated Value

x	integer	6
y	integer	-3
a	integer	0
b	number	45
y1	number	-3
y2	number	3
x1	number	6
x2	number	-6

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1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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3. Gap Gap 2. Number entry
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4. Gap Gap 3. Number entry
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Corresponding value of $x=$ Gap 3.

Advice

Rearranging the first equation gives $x=\var{x+2y}-2y$

Substituting this expression for $x$ into our second equation gives $(\var{x+2y}-2y)^2+y^2=\var{x^2+y^2}$

Expanding brackets gives $\simplify[]{{(x+2y)^2}-{4*(x+2y)}}$ $y+4y^2+y^2=\var{x^2+y^2}$

Rearranging gives $\simplify[]{5y^2-{4*(x+2y)}y-{x^2+y^2-(x+2y)^2}}=0$

Solving by factorising or using the quadratic formula gives $y=\frac{\var{4a} \pm \sqrt{\var{16a^2+20(b-a^2)}}}{10}$

Hence $y = \var{y1}$ or $\var{y2}$

and the corresponding values of $x$ are $\var{x1}$ and $\var{x2}$ respectively (found by substituting each value of $y$ into $x+2y=\var{x+2y}$ )

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Taxonomy: mathcentre

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Taxonomy: Context

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Simon Thomas 5 years ago

Simon Thomas 5 years ago

Error in variable testing condition

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Generated value: `integer`

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Quadratic simultaneous equations

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Simon Thomas 5 years ago

Simon Thomas 5 years ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`