Simultaneous Equations Involving Quadratic Functions

Q1.

Rearranging:

Substituting in (1):

Expanding (1) :

Tidying up :

Factorising:

Substituting for "x" (twice) in equation (2):

The pairs of values for "x" and "y" are therefore:

Q2.

Rearranging (2)

Substituting the transposed equation (2) into equation (1):

Expanding the left hand side of (1) (subst):

Rearranging to produce the Quadratic Equation:

Using the Quadratic Formula to establish the roots of the Quadratic Equation:

We have:

So:

Therefore:

Substituting (twice) for "x" in equation (2) :

The pairs of values for "x" and "y" are therefore:

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