Fsc Part 1 Mathematics (Complete Solution)

Q3
Find x and y if

(i)  
 
x+3 1
-3 3y-4
 
  = 
 
2 1
-3 2
 
 

SOLUTION:

       
 
x+3 1
-3 3y-1
 
  = 
 
2 1
-3 2
 
 

using definition of equality of matrices, we have

x+3=2

x=2-3

x=-1

and

3y-1=2

3y=2+1

3y=3

y=1

 

 (ii)  
 
x+3 1
-3 3y-4
 
  = 
 
y  1
-3 2x
 
 

SOLUTION:

                
 
x+3 1
-3 3y-4
 
  = 
 
y 1
-3 2x
 
 

using definition of equality of matrices, we have

x+3=y

x-y=-3     -----------------------------(i)

and

3y-4=2x

2x-3y=-4   ---------------------------(ii)

multiply 2 by (i)

2x-2y=-6    -----------------------------(iii)

subtract (ii) from (iii)

2x-3y-2x+2y= -4+6

-y=2

y=-2

put y=-2 in (i)

x+2=-3

x=-3-2

x=-5

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