Consider the equation 6 x + 3 y = 9. which equation, when graphed with the given equation, will form a system with infinitely many solutions?
y + 2 x = 3
y + 2 x = 9
y = 2 x + 3
y = -2 x + 9

This question involves minimal work. We just need to convert from standard form to slope-intercept form and look for identical equations.

Let’s start by moving the x term to the other side

6x + 3y = 9
3y = -6x + 9

Now divide by 3 to isolate the y-value

3y = -6x + 9
y = -2x + 3

Now this should be your final answer, but since your options do not contain the correct answer in slope-intercept form, we can convert it back to standard form to get our final answer. [note: all this work could have been avoided if we noticed that the equation from the problem was divisible by 3, but this is good practice for converting between forms; I promise it will help in future math classes]

y = -2x + 3

Subtract the x term from both sides

y + 2x = 3

And there you have it! Your final answer is option A, y + 2x = 3