Determine the number of solutions to the system of linear equations

Question

2X plus Y equals six
4X plus 2Y equals eight

Answer 1

This system of equations is equivalent to:
1) 2X + Y = 6
2) 4X + 2Y = 8

Simplifying the second equation by dividing both sides by 2, we get:
4X + 2Y = 8
2X + Y = 4

Notice that the second equation is just the first equation divided by 2. This means that the two equations represent the same line, and therefore have infinitely many solutions.