Question

5.4 solving systems of equations by elimination quiz

you must always multiply both equations before using elimination.

true
false

Explanation:

Analyze the statement

The statement claims: "You must always multiply both equations before using elimination." We need to evaluate if this is mathematically true or false.

Understand the elimination method

Using the Elimination Method, the goal is to add or subtract the equations to eliminate one variable. This requires the coefficients of one variable to be opposites or identical.

Evaluate necessity of multiplication

Sometimes, coefficients are already opposites, such as:

$$
LATEXBLOCK0
$$

Here, we can add them directly to eliminate \(y\) without any multiplication.

Evaluate multiplying one equation

Other times, we only need to multiply one equation to match coefficients, such as:

$$
LATEXBLOCK1
$$

Multiplying the second equation by \(2\) is sufficient; we do not need to multiply both.

Determine the truth value

Since we do not always have to multiply both equations, the statement is false.

Answer:

• True
• False (Correct answer)