When solving ordinary – linear –
simultaneous equations we multiply the equations by constant factors
to make the coefficient of some variable the same in magnitude, then
add or subtract the equations to eliminate that variable.
For example, solve
(1)
(2)
(1)*2-(2)*3 eliminatesto
give
Substitution of this value ofinto
(1) to find a gives
If one of the equations is a quadratic we
may not be easily able to rearrange the equations to easily eliminate
one of the variables and solve the equations. But we can rearrange
one of the equations – usually the linear one - to make
eitherorthe
subject.
Example:
(1)
(2)
Rearrange (1) to makethe
subject:and
substitute this into (2) to get
To solve the last equation we can either
factorise or use the quadratic formula.
By factorising:or
IffromIffrom
By using the quadratic formula:
hence
or
3.
As before , substitute these values ofback
into (1) to obtain
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