Question

Solve ;-

$2u \: + 5v = \frac{1}{4}$
$3u + 6v = \frac{1}{3}$

Answer 1

heya mate here is your answer ..>>

2u + 5v = 1/4 -------(i)

3u + 6v = 1/3--------(ii)

by using elemination method ,

multiplying 3 on equation 1 and 2 on equation 2

6u + 15v = 3/4-----(iii)

6u + 12v = 2/3-----(Iv)

subtracting equation III and iv

6u+15v-6u-12v = 3/4-2/3

$3v = \frac{9 - 8}{12} = \frac{1}{12}$

so, v = 1/36

putting the value of v in equation 1

2u + 5×1/36 = 1/4

2u = 1/4 - 5/36 = 9-5/36 = 4/36 = 1/9

2u = 1/9

u = 1/9 × 1/2 = 1/18

so the value of v is 1/36 and the value of u is 1/18

hope it helps you

Answer 2

Hey!

Solve :

2u + 5v = 1/4

3u + 6v = 1/3

Now,

=> 2u + 5v - 1/4 = 0

=> 8u + 20v - 1 = 0 ------(1)

Again,

3u + 6v = 1/3

=> 9u + 18v - 1 = 0 ------(2)

So, (9)×(1) then,

(9)×(8)u + (9)×(20)v - 9 = 0

=> 72u + 180v - 9 = 0 ------(3)

and,

(8)×(2) then,

(8)×(9)u + (8)×(18)v - 8 = 0

=> 72u + 144v - 8 = 0 -----(4)

(3) - (4)

72u + 180v - 9 - (72u + 144v - 8 ) = 0×0

=> 72u + 180v - 9 - 72u - 144v + 8 = 0

=> 180v - 144v -9 + 8 = 0

=> 36v - 1 = 0

=> 36v = 1

=> v = 1/36

putting the value of 'v' in (1)

8u + 20v - 1 = 0

=> 8u + 20(1/36) - 1 = 0

=> 8u + 5/9 - 1 = 0

=> 72u + 5 - 9 = 0

=> 72u - 4 = 0

=> 72u = 4

=> u = 4/72

.•. u = 1/18

So, hence, u = 1/18 and v = 1/36