Question

Given the equation 2x + 4y = -10, write the equation of a line that would have the same solution set. Justify your answer.

Answer 1

To find an equation with the same solution set as 2x + 4y = -10, multiply both sides of the original equation by a non-zero constant. For example, using 3 as the constant gives the new equation 6x + 12y = -30, which has the same solution set.

Step-by-step explanation:

To write an equation that has the same solution set as the given equation 2x + 4y = -10, we need to create an equation that is a multiple of the original. Essentially, we can multiply both sides of the equation by any non-zero constant, and the solution set will remain unchanged.

Let's use the constant 3. Multiplying both sides of the equation by 3 yields:

3(2x) + 3(4y) = 3(-10)

This simplifies to:

6x + 12y = -30

This new equation 6x + 12y = -30 has the same solution set as the original equation because it represents the same line, simply scaled up by a factor of 3.