(х-4)(у-6)=0 у-4/х+у-8=2

To solve the system of equations:

1. (x-4)(y-6) = 0
2. y - (4/x) + y - 8 = 2

Let's solve one equation at a time.

Equation 1: (x-4)(y-6) = 0

To find the solutions for equation 1, we need to set each factor equal to zero and solve for x and y separately.

Setting x-4 = 0: x = 4

Setting y-6 = 0: y = 6

So one solution to equation 1 is (x,y) = (4,6).

Equation 2: y - (4/x) + y - 8 = 2

To simplify this equation, let's combine like terms: 2y - (4/x) - 8 = 2

Let's get rid of the fraction by multiplying every term in the equation by x: 2xy - 4 - 8x = 2x

Let's move all terms to one side of the equation: 2xy - 8x - 2x - 4 = 0

Combine like terms: 2xy - 10x - 4 = 0

Now, we can substitute the value of x from equation 1 into equation 2: 2(4)y - 10(4) - 4 = 0 8y - 40 - 4 = 0 8y - 44 = 0

Move -44 to the other side: 8y = 44

Divide both sides by 8: y = 44/8 y = 5.5

So the solution to equation 2 is y = 5.5.

Therefore, the system of equations has two solutions: (x, y) = (4, 6) and (x, y) = (4, 5.5).