Is there a solution to the simultaneous equations three 𝑥 plus four 𝑦 equals 10 and three 𝑥 plus four 𝑦 equals negative 12? If yes, what is it?
Well, let’s try to solve. I noticed that the 𝑥 and 𝑦 in both of these equations have the same coefficient, so let’s try to solve by elimination. Here, we would say three 𝑥 minus three 𝑥 equals zero. Four 𝑦 minus four 𝑦 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: There’s no solution. These lines never cross.