04 - Simultaneous Equations

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

) Class: ___________

Q1)

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.

Q2)

Given that A  

Q3)

(i)

 1 1  2 1   2 0 , B    and C   ,  4 5  1 0   1 0 find the matrix P such that APB  C .

(iii)

Show that the matrix P is singular.

Solve the simultaneous equations 2x  3y  6

 2 x  1 Q4)

Q5)

Q6)

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  3 2  , write down the expression for the inverse If M denotes the matrix   p 4 matrix M −1 and hence find the solution set of the simultaneous equation 3 x + 2y = 2 px + 4 y = q when p = q = 5 .  5 4  . Hence, determine the coordinates Find the inverse of the matrix   −1 2  of the point of intersection of the lines 5x + 4y = 6 and 2y – x = 24.

© Jason Ingham 2009

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