Answer:
x = 5y + 6.5 from the second equation is probably the 'best' variable to use (but it's quite subjective, and any of the four possibilities would work).
Explanation:
First of all, let me say that best is subjective. And I don't know the context this question is coming from, or what and how you've been taught. The fact is, if you're careful with signs and fractions, you can solve this system of equations by solving either equation for either variable. So with that said, let me give you my opinion.
See all the multiples of 3 in the first equation? That equation isn't in its simplest form, so divide the whole thing by 3 to make it become:
x + 2y = 3
Do you see how that worked? Just divide each term of the original equation to get the new terms I wrote. It's the same equality, just simpler now.
And from there you should be able to see that you can easily solve for either x or y:
- x = -2y + 3
- y = (-x + 3)/2
Which of those would you rather work with as a substitution?
I vote for x = -2y + 3
Now let's look at the second equation: can you simplify it? Looks like we could divide by 2 and get:
x - 5y = 6.5
Solve for x & y:
- x = 5y + 6.5
- y = (x - 6.5)/5
Now which of those would you rather work with?
I vote for x = 5y + 6.5
So we looked at both equations, and for each one we decided that "the best variable" to solve for would probably be x. But now let's decide between them:
Which one of those would you say is BEST? My vote would be for the second one. Why? Because that negative sign in the first one might trip us up. Other than that, though, it's an easier one to work with (2 vs. 5 for the y coefficient, and the constant term of 3 is easier to work with than 6.5.)
But remember: you could use ANY of those 4 substitutions to solve the equations. Just be careful with signs and arithmetic!