16569297-04-simultaneous-equations.doc

St Joseph’s Institution Secondary Four Mathematics TOPIC − Simultaneous Equations Name:_____________________________________ ( Q1)

Q2)

Find the range of values of m such that the line y = mx + 3 does not meet the circle with equation x2 + y2 – 2x – 1 = 0.

1 1� -2 1 � � � �2 0 � ,B=� Given that A = � � �and C = � �, 4 5� 1 0� � �-1 0 � � (i) find the matrix P such that APB = C . (iii)

Q3)

Show that the matrix P is singular.

Solve the simultaneous equations 2x + 3y = 6

( 2 x + 1) Q4)

) Class: ___________

2

+ 6 ( y - 2 ) = 49 2

Find the values of k for which the following simultaneous equation have no solution 2 x - 3ky = 1

4 x + ( k + 2) y = 5

Q5)

3 p

If M denotes the matrix 

2  , write down the expression for the inverse 4 

matrix M -1 and hence find the solution set of the simultaneous equation when

Q6)

3 x + 2y = 2 px + 4 y = q p =q =5.

 5  -1

Find the inverse of the matrix 

4  . Hence, determine the 2 

coordinates of the point of intersection of the lines 5x + 4y = 6 and 2y – x = 24.

© Jason Ingham 2009

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