Question

13 - 6x - y = 0; options: y = -6x + 13, -6x - y = -13, 6x + y = 13, 13 - 6x = y

Explanation:

Step1: Analyze the original equation

The original equation is \(13 - 6x - y = 0\). We need to transform it to match one of the given options.

Step2: Rearrange the original equation

Start with \(13 - 6x - y = 0\). Add \(6x + y\) to both sides: \(13=6x + y\), which is the same as \(6x + y = 13\). Also, we can solve for \(y\): subtract \(6x\) from both sides, \(y=13 - 6x\) or \(y=-6x + 13\). And if we multiply the original equation by - 1: \(-13 + 6x + y = 0\), then \(6x + y=13\) (same as before) or \(-6x - y=-13\) (by moving 13 to the other side and multiplying by - 1). But the question is about which equation is equivalent. Let's check each option:

• Option 1: \(y = - 6x+13\) is equivalent (solved for \(y\)).
• Option 2: \(-6x - y=-13\) is equivalent (multiply original by - 1).
• Option 3: \(6x + y = 13\) is equivalent (rearranged).
• Option 4: \(13 - 6x=y\) is equivalent (solved for \(y\)).

But maybe the question is about which is the standard form or a direct rearrangement. If we take the original \(13-6x - y = 0\), moving terms: \(6x + y=13\) (Option 3) is a standard linear equation form \(Ax + By = C\).

Answer:

The correct equation (taking the third option as an example of a standard form) is \(6x + y = 13\) (the third blue box with \(6x + y = 13\))