Rodrigo is looking at the system below.

2x + 3y = 9

x - 8y = 11

to solve, he first multiplied the second equation by two and then subtracted the equations.

is rodrigo correct? justify your answer. if incorrect, describe the error

The system of equations is
2x + 3y = 9          (1)
 x - 8y = 11            (2)

Multiply (2) by 2 and subtract from (1).
2x + 3y - 2(x - 8y) = 9 - 2*11
2x + 3y - 2x + 16y = -13
19y = - 13
   y = - 13/19

Rodrigo is correct because he eliminated x and solved for y.

Calculate x from (2).
x = 11 + 8y
   = 11 + 8*(-13/19)
   = 105/19

The solution is x = 105/19, y = -13/19.

Verify the solution by substituting in (1).
2x + 3y = 2*(105/19) + 3*(-13/19) = 9
The solution is correct.

Rodrigo is correct because he eliminated x and solved for y.
The solution checks out to be correct.

Angle K is congruent to itself, due to the reflexive property

Step-by-step explanation:

Given:  ΔLKM is similar to ΔNOM

To find: statement that is not used to prove that ΔLKM is similar to ΔNOM

Solution:

Two figures are said to be congruent if they have same shape and same size.

Two figures are said to be similar if they have same shape but different size.

If two figures are similar then their corresponding angles are equal.

As ΔLKM ΔNOM,

So, statement that can be used to prove that ΔLKM is similar to ΔNOM is ''Angle K is congruent to itself, due to the reflexive property''