Question

solve the following equations:
a) 3x-4y=7; 5x+2y=3
b) 5x+7y=17; 3x-2y=4
c) x -2y= -10; 3x-2y=-12​

Answer 1

(a). 3x-4y=7

5x+2y=3

D=|3 -4|=6+20=26

|5 2|

Dx=|7 -4|=14+12=26

|3 2|

Dy=|3 7|=9-35=-26

|5 3|

by cramers rule

x=Dx/D=26/26=1

y=Dy/D=-26/26=-1

(x,y)=(1,-1)

(b). Given simultaneous equations are ,

5x + 7y = 17

multiply both sides with 2 , we get

10x + 14y = 34 ---( 1 )

3x - 2y = 4

multiply both sides with 7 , we get

21x - 14y = 28 ---( 2 )

Add ( 1 ) & ( 2 ) , we get

31x = 62

=> x = 62/31

=> x = 2

substitute x = 2 in equation ( 1 ) ,

10 × 2 + 14y = 34

=> 20 + 14y = 34

=> 14y = 34 - 20

=> 14y = 14

=> y = 14/14

y = 1

Therefore ,

x = 2 , y = 1

Answer 2

hope it is helpful..........