Exploring Systems of Equations through Elimination

Why is it important to write equations in standard form when using the elimination method?

• To make substitution easier

• To avoid fractions

• To ensure coefficients are integers

• To align variables for elimination

What does the term 'additive inverses' refer to in the context of the elimination method?

• Two numbers that subtract to zero

• Two numbers that are equal

• Two numbers that add up to zero

• Two numbers that multiply to one

In the elimination method, why might you choose to align the Y variables instead of the X variables?

• Because Y variables are always easier to eliminate

• Because it simplifies the equations

• Because X variables cannot be eliminated

• Because the coefficients of Y are already additive inverses

What is the first step after obtaining additive inverses in the elimination method?

• Divide the equations

• Add the equations

• Multiply the equations

• Subtract the equations

When solving 5x = 10, what is the value of x?

• 10

• 2

• 5

• 1

Why might you need to multiply one of the equations by a negative number in the elimination method?

• To simplify the equation

• To create additive inverses

• To eliminate fractions

• To make the coefficients equal

What is the least common multiple of 2 and 3?

• 3

• 6

• 5

• 2

In the elimination method, what should you do if both X and Y variables cancel out?

• Multiply the equations again

• Divide the equations

• Check for infinite solutions

• Add a constant to one equation

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

• The equations are incorrect

• There are infinite solutions

• There is one unique solution

• There is no solution

Why is it beneficial to eliminate fractions in the elimination method?

• To ensure the coefficients are integers

• To make the equations easier to solve

• All of the above

• To avoid dealing with decimals