6x + 3y = -4 15x + 7y = -8 how many solutions does the system of equations have?
1 answer:
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Answer:
= {1,3,5,7,9,....}
= {1,2,4,5,7,8,10,11,13,14......}
= {1,2,3,4,5}
= {10,11,12,13,14,15,......}
Step-by-step explanation:
Solution:
It is given that, Universal set is the set of all Natural Numbers.
and
Set A, Set B, Set C, Set D are subsets of Universal set.
A = {x:x is even natural numbers} = {2,4,6,8,10,.....}
B = {x:x ∈ N and x is a multiple of 3} = {3,6,9,12,15,....}
C = {x:x∈ N and x < 5} = {6,7,8,9,10,.....}
D = {x:x ∈ N and x > 10} = {1,2,3,4,5,6,7,8,9}
U = {1,2,3,4,5,6,7,8,9,10,11,........}
Complements:
= U-A = {1,2,3,4,5,6,7,8,9,10,11,........} - {2,4,6,8,10,.....}
= {1,3,5,7,9,....}
= U-B = {1,2,3,4,5,6,7,8,9,10,11,........} - {3,6,9,12,15,....}
= {1,2,4,5,7,8,10,11,13,14......}
= U-C = {1,2,3,4,5,6,7,8,9,10,11,........} - {6,7,8,9,10,.....}
= {1,2,3,4,5}
= {1,2,3,4,5,6,7,8,9,10,11,........} - {1,2,3,4,5,6,7,8,9}
= {10,11,12,13,14,15,......}