Aset of equations is given below:
equation r: y = 5x + 10
equation s: y = 5x + 5
which of the following options is true about the solution to the given set of equations?
one solution
two solutions
infinite solutions
no solution

Option D. No solution

Step-by-step explanation:

In the question we have been given two equations of the line as

R: y = 5x + 10

S: y = 5x + 5

In these two linear equation which are in form of y = mx + c

Where m is the slope of line.

Here in equation R: slope of the line= 5

         in equation S: slope of line = 5

Therefore both the lines have same slope means both the lines are parallel to each other and they don't intersect.

This clearly speaks that both the equations have no solutions.

Option D. is the correct option.

∠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.