Where do the lines xy = 0 and 6x + 5y = 22 intersect?

To find the intersection point of the lines represented by the equations xy = 0 and 6x + 5y = 22, we first analyze each equation.

The equation xy = 0 describes two lines: one where x = 0 (the y-axis) and one where y = 0 (the x-axis).

The second equation, 6x + 5y = 22, can be rewritten to find y in terms of x:

5y = 22 - 6x
y = (22 - 6x) / 5

Now we can find the points where this line intersects the two lines represented by the first equation.

1. For x = 0:

y = (22 - 6(0)) / 5 = 22 / 5 = 4.4

This gives us the point (0, 4.4).

2. For y = 0:

0 = (22 - 6x) / 5
=> 22 - 6x = 0
=> 6x = 22
=> x = 22 / 6 = 11/3 ≈ 3.67

This gives us the point (11/3, 0).

Thus, the lines intersect at the points (0, 4.4) and (11/3, 0).