Question

Nathan solves the following system of equations using the elimination method.

−2x+3y=64x−6y=−12

He chooses to eliminate the variable x.

Which statement correctly describes his process and solution?

Responses

Nathan multiplies −2x+3y=6 by 2 and then adds the equations. He finds the result is an identity, so there are infinitely many solutions.

Nathan multiplies −2x+3y=6 by 2 and then subtracts the equations. He finds the result is an identity, so there are infinitely many solutions.

Nathan multiplies −2x+3y=6 by 2 and then adds the equations. He finds the result is a contradiction, so there is no solution.

Nathan multiplies −2x+3y=6 by 2 and then subtracts the equations. He finds the result is a contradiction, so there is no solution.

Answer 1

The correct answer is "Nathan multiplies −2x+3y=6 by 2 and then adds the equations. He finds the result is an identity, so there are infinitely many solutions."

Explanation:
Multiply the first equation by 2, and multiply the second equation by 1.
2(−2x+3y=6)
1(4x−6y=−12)
Becomes:
−4x+6y=12
4x−6y=−12
Add these equations to eliminate x:
0=0

therefore there are infinitely many solutions.