Question

Find the number of ordered pairs of integers(X,y) such that (2x+y)(5x+3y)=7

Answer 1

it is given that , (2x + y)(5x + 3y) = 7

it can be written as, (2x + y)(5x + 3y) = 7 × 1 = 1 × 7

case 1 : (2x + y)(5x + 3y) = 7 × 1

so we can assume, (2x + y) = 7 and (5x + 3y) = 1

now, 3(2x + y) - (5x + 3y) = 3 × 7 - 1

or, 6x + 3y - 5x - 3y = 20

or, x = 20 and y = 7 - 2(20) = -43

hence, one ordered pair = (20, -43)

case 2 : (2x + y)(5x + 3y) = 1 × 7

so we can assume, (2x + y) = 1 and (5x + 3y) = 7

now, 3(2x + y) - (5x + 3y) = 3 × 1- 7

or, 6x + 3y - 5x - 3y = -4

or, x = -4 and y = 1 - 2x = 1 - 2(-4) = 9

hence, one more ordered pair = (-4, 9)

here we see that there are two ordered pairs (20, -43) and (-4,9) follow given condition.

so, answer = (20, -43) and (-4,9)

Answer 2

Step-by-step explanation:

Dimensional Formula of Resistance

The dimensional formula of resistance is given by,

M1 L2 T-3 I-2