Which statement correctly identifies the mistake Joe made? in step 5, Joe should have added 1 to both sides of the equation instead of dividing both sides of the equation by --1. In step 2. Joe should have multiplied the first equation by 2 instead of by 3. in step 4, Joe simplified 27 + (-20) as 7 instead of simplifying to -7. In step 3, Joe multiplied the term -2y by 2 instead of by-2.

This question is incomplete as it lacks the actual question. The question describes how Joe solved a system of equations step-by-step using elimination method. The steps used by Joe are as follows:

1. The equations given are: 2x + y = 9 and 3x - 2y = 10.

2. Multiply the first equation by 3 to get 6x + 3y = 27

3. Multiply the second equation by -2 to get -6x - 4y = -20

4. Add the equations to get -y = 7

5. Divide both sides of the equation by -1 to get y = -7

The statement that correctly identifies the mistake Joe made is: In step 3, Joe multiplied the term -2y by 2 instead of by-2.

Step-by-step explanation:

Elimination method of solving a simultaneous equation in Mathematics involves removing one variable in order to solve another variable. In this case of equations:

2x + y = 9

3x - 2y = 10

Joe eliminates the x variable in order to solve for the y variable first. To do this;

- In step 2, he correctly multiplies the first equation by 3 to get 6x + 3y = 27

- In step 3, he multiplies the second equation by -2 to INCORRECTLY get -6x - 4y = -20

Joe made a mistake in this step 3 because he multiplied -2y in the original equation (3x - 2y = 10) by 2 and not -2. He should have gotten -6x + 4y = -20 if he multiplied by (-2). That is (-2 × -2y) to give +4y.