Methods2024 NHT Exam 1 · Q2Tech-free5 marks

Simultaneous linear equations with a parameter

Consider the simultaneous linear equations

$ax + (2 - a)y = 3$ $x + ay = \frac{2a+1}{2}$

Find the value of $a$ for which there are infinitely many solutions.

3 marks

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Find the values of $a$ for which there is a unique solution.

1 mark

Hints, answer checking and worked solutions come with a Season Pass.

Find a value of $a$ such that the lines meet at right angles.

1 mark

Hints, answer checking and worked solutions come with a Season Pass.