Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
minus, x, plus, y, equals, 8
−x+y=
8
2, x, minus, 2, y, equals, minus, 14
2x−2y=
−14
To determine the number of solutions, we will solve the system of equations using elimination or substitution.
First, let's solve the system of equations using elimination.
From the first equation, we have:
-x + y = 8
From the second equation, we have:
2x - 2y = -14
Let's multiply the first equation by 2 to cancel out the x term:
-2x + 2y = 16
Now we can add the two equations together:
(-2x + 2y) + (2x - 2y) = 16 + (-14)
0 = 2
The resulting equation is 0 = 2, which is not true. This means there are no solutions to the system of equations.