This system has one solution, which is x = 6 and y = 1.
Step-by-step explanation:
Solving by separation:
Three cases:
If we end up with cx(or cy) = d, in which c is different of zero, the system has one solution.
If we end up with cx = d, in which c is zero and d is zero, the system has infinite solution.
If we end up with cx = d, in which c is zero and d is not zero, the system does not have any solution.
Solving this system:
2x - 4y = 8
x + y = 7
So
x = 7 - y
Replacing in the first equation
2(7 - y) - 4y = 8
14 - 2y - 4y = 8
-6y = -6
6y = 6
None of the coefficients are zero, so one solution
y = 1
x = 7 - y = 7 - 1 = 6
This system has one solution, which is x = 6 and y = 1.
