Question

16.
Find the integral values of x, y and z, if
i) 243x + 198y=9 ii) 61x - 40y=1
) 10x - 8y= 42
(iv) 6x+10y +15z=-1:1.​

Answer 1

Answer:

Step-by-step explanation:

Find the integral values of x, y and z, if

i) 243x + 198y=9 ii) 61x - 40y=1

) 10x - 8y= 42

(iv) 6x+10y +15z=-1

i) 243x + 198y=9

Dividing by 9

27x + 22y = 1

x = 9  y = -11

ii) 61x - 40y=1

61x = 40y + 1

40y will end with 0

=> 40y + 1 will end with 1

61 will end with 1 when multiplied with 11 , 21 , 31

61 * 21 = 40 * 32 + 1

1281 = 1280 + 1

x = 21 & Y = 32

or if y is -ve then

40y + 1 will end with 9 (-ve number)

x can be - 9 , -19 , -29 ......... to end with 9

61*(-19) = 40(-29) + 1

-1159 = -1160 +1

x = -19 & Y = -29

10x - 8y= 42

5x - 4y = 21

x = 1 & y =  -4

x = 5  & y  = 1

x = 9 & y = 6