To help solve the system of equations by elimination and complete the table, I need the specific system of equations you're working with. However, I will provide a general step-by-step method for solving a system using elimination. Once you give the equations, I can update the drop-down items accordingly.

Here’s the general structure:

Step 1: Label the equations

Let the two equations be:

1. Equation 1: $a_1x + b_1y = c_1$
2. Equation 2: $a_2x + b_2y = c_2$

Step 2: Adjust the equations to eliminate one variable (Drop Down 1)

We multiply one or both equations by a constant to make the coefficients of either $x$ or $y$ the same, so we can eliminate that variable by addition or subtraction.

• Drop Down 1: Multiply Equation 2 by a constant to match a variable's coefficient with Equation 1.

Step 3: Add or subtract the equations (Drop Down 2)

Add or subtract the equations to eliminate one variable:

• Drop Down 2: Indicate whether the equations are added or subtracted.

Step 4: Solve for one variable (Drop Down 3 and Drop Down 4)

After elimination, you’ll get a new equation with one variable. You solve for that variable by dividing both sides by its coefficient.

• Drop Down 3: The coefficient you divide by.
• Drop Down 4: The variable you're solving for (either $x$ or $y$).

Step 5: Solve for the remaining variable

Once you find one variable (e.g., $y$), substitute it back into one of the original equations to find the other variable (e.g., $x$).

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Could you provide the specific system of equations you are working on? That will allow me to give a more detailed and tailored answer to fill out the drop-downs.

Related questions:

1. What is the system of equations you are solving?
2. Would you like help solving the system step by step?
3. Is there a particular variable you prefer to eliminate first?
4. Are both equations in standard form, or should we rearrange them?
5. Do you need clarification on elimination methods?

Tip: When eliminating, it’s often easier to eliminate the variable with the smallest coefficients to avoid large numbers or fractions.