Answer: Inconsistent System
Step-by-step explanation:
If you solve 10x-2y = 12 for y, you get
10x = 12+2y
10x-12 = 2y
2y = 10x-12
y = (10x-12)/2
y = 5x-6
The equation 10x-2y = 12 is the same as y = 5x-6.
The system of equations consists of y = 5x+2 and y = 5x-6. Both have the same slope (m = 5) but different y intercepts (2 and -6). This means the graphed lines will be parallel. Parallel lines never intersect, so there are no solutions. A system is considered inconsistent if it has no solutions.