System of equations with no solution

choose all of the system of equations which have no solution.

x + 2y = 10 and 2y = 6 + 5x
x = 8 − y and y = 6 + 5x
3x + 2y = 5 and 2y = 6 − 3x
3x = 2 − 4y and 4y = 7 − 3x

C. 3x + 2y = 5 and 2y = 6 - 3x  & D. 3x = 2 − 4y and 4y = 7 − 3x , have no solution! (:  

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.