Systems of Equations - Elimination Part 2 Guided Notes

What is the first step in solving systems of equations by elimination with unmatching coefficients?

• Solve for one variable directly

• Multiply equations to create matching coefficients

• Add or subtract the equations immediately

• Ensure the variables are aligned

How do you create matching coefficients for elimination?

• Divide one equation

• Subtract the equations

• Multiply one or both equations

• Rearrange the equations

When solving by elimination, what do you do after aligning the variables and before adding the equations?

• Divide both equations by the same number

• Multiply equations to create opposite coefficients

• Substitute one variable into the other equation

• Solve for one variable

What happens to the variables when you add equations with opposite coefficients?

• One variable is eliminated

• They are multiplied

• They become constants

• Nothing changes

In the context of elimination, what does creating opposite coefficients accomplish?

• It simplifies the equations

• It eliminates one variable when equations are added

• It makes the variables equal

• It isolates one variable

What does it mean if, after elimination, you get a statement like 0=0?

• The system has no solution

• The equations are incorrect

• The system has exactly one solution

• The system has infinite solutions

What should you do if the variables in the system of equations are not aligned?

• Eliminate a variable immediately

• Multiply the equations

• Add the equations as they are

• Rearrange one or both equations

What is the result of a system of equations if, after elimination, you are left with a false statement?

• No solution

• One solution

• Two solutions

• Infinite solutions

How can you tell if a system of equations has exactly one solution when using elimination?

• If you get a true statement like 0=0

• If you end up with a variable equal to a number

• If you get a false statement

• If the coefficients cannot be matched

What is the significance of multiplying both equations in a system when using elimination?

• To align the variables correctly

• To create the same coefficient for one variable

• To simplify the equations for easier solving

• To directly solve for one variable