How many solution(s) does the system of equations have?

Question

−5x+y=−18
10x−2y=36(1 point)

Answer 1

This system of equations has one unique solution.

To see why, we can simplify the second equation by dividing both sides by 2:

10x - 2y = 36

becomes

5x - y = 18

Now we have two equations:

-5x + y = -18

5x - y = 18

Adding these equations eliminates the y terms:

0 = 0

This means the two equations are equivalent and represent the same line. In other words, the two equations have infinitely many solutions (every point on the line is a solution).

But if we look back at the original system, only one of the equations has a unique solution (the first equation). Therefore, the system as a whole has only one unique solution.