SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Algebra, MET1 2022 VCAA 3

Consider the system of equations

Determine the value of for which the system of equations above has an infinite number of solutions.   (3 marks)

Show Answers Only

for infinite solutions

Show Worked Solution

Making the subject of each equation:

   
  (1)
     
 
  (2)

 
From equations (1) and (2)

and
 

An infinite number of solutions occur when

 
 
 
 

 

 

Let and be the -intercepts of equations (1) and (2)

then   and 
 

 
 
 
   

 
for infinite solutions and only value to satisfy both equations.


♦ Mean mark 50%.
MARKER’S COMMENT: Students are reminded to always use the correct variables.

Algebra, MET1 2011 VCAA 6

Consider the simultaneous linear equations

where is a real constant.

  1. Find the value of for which there are infinitely many solutions.  (3 marks)
  2. Find the values of for which there is a unique solution.  (1 mark)
Show Answers Only
Show Worked Solution

a.  

♦ Mean mark 39%.
MARKER’S COMMENT: A number of solutions are possible here, including using the determinant.

 

   

 

 
 
 
 
   

 

 

b.  

♦♦ Mean mark 33%.