### Video Transcript

Is there a solution to the simultaneous equations three ๐ฅ plus four ๐ฆ equals 10 and three ๐ฅ plus four ๐ฆ equals negative 12? If yes, what is it?

Well, letโs try to solve. I noticed that the ๐ฅ and ๐ฆ in both of these equations have the same coefficient, so letโs try to solve by elimination. Here, we would say three ๐ฅ minus three ๐ฅ equals zero. Four ๐ฆ minus four ๐ฆ equals zero. 10 minus negative 12 equals 12.

Trying to solve this problem by elimination produces zero equal to negative 12. zero is not equal to negative 12. This tells us two things. First, it tells us that there is no solution here. It also tells us that these two equations represent parallel lines. Parallel lines do not have a solution because they never cross; they never intersect.

But to answer this question, we simply need to say: Thereโs no solution. These lines never cross.