Question

If the lines 3x + 4y = 7, 5x – y = 4 and ax + by = 12 are concurrent, then number of ordered pairs (a, b), when a and b are non-negative integers is ??
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Answer 1

Step-by-step explanation:

all the lines intersect at a point so,

from 1st line,

3x = 7 - 4y

x = (7-4y) / 3

replacing in second line,

(35 - 20y) / 3 - y = 4

35 - 20y - 3y = 12

23y = 23

y = 1

therefore x = 1 ( placing value of y in above equation of x)

therefore replacing x and y in 3rd line,

a+b = 12

now a and b are non negative so,

( 1,11) , ( 2,10) ,( 3,9), ( 4,8), (5,7), (6,6) , (7,5), ( 8,4) , (9,3), ( 10,2) , (11,1)

hence there are 11 ordered pairs for (a,b)