How many solutions does this system have? 2x-4y=8 x+y=7

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.