Question

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

Answer 1

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.

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