Solve for this problem using elimination.

There is no solution to this system.

Step-by-step explanation:

To solve this problem solve the second equation for y.

2x + y = 9

y = -2x + 9

Now that we have the value of y, we can put that in for y in the first equation and solve for x.

3y = -6x + 4

3(-2x + 9) = -6x + 4

-6x + 27 = -6x + 4

27 = 4

Because this is a false statement, we know that this system has 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.