(х-4)(у-6)=0 у-4/х+у-8=2

To solve this system of equations, we can use the method of substitution.

1. (х-4)(у-6) = 0

Let's consider the two possible cases:

Case 1: х-4 = 0 Solving for х, we get: х = 4

Substituting this value back into the second equation: у - 4/(4) + у - 8 = 2 у - 1 + у - 8 = 2 2у - 9 = 2 2у = 11 у = 11/2

So, one solution is (х, у) = (4, 11/2).

Case 2: у - 6 = 0 Solving for у, we get: у = 6

Substituting this value back into the second equation: у - 4/х + у - 8 = 2 6 - 4/х + 6 - 8 = 2 12 - 4/х = 2

To solve for х, we can multiply both sides by х to get rid of the denominator: 12х - 4 = 2х 10х = 4 х = 4/10 х = 2/5

So, another solution is (х, у) = (2/5, 6).

Therefore, the system of equations has two solutions: (4, 11/2) and (2/5, 6).