How many solutions does the system formed by x-y=6 and ay-ax+6a=0 have for a nonzero number a? Explain.

infinitely many

Step-by-step explanation:

Just rearrange the second equation:

a(y - x + 6) = 0

y - x + 6 = 0

y - x = -6

x - y = 6

You have two equations that are identical. The number of (x,y) pairs satisfying "both" equations is just the number of pairs satisfying the first one. (Think about it, satisfying one is satisfying both.)

There are infinitely many (x,y) pairs satisfying x - y = 6, so answer is "infinitely many solutions."

b

2

−

b

b

3

+

7

b

2

+

14

b

+

6

%

−

3

b

3

+

7

b

2

+

14

b

+

6

%

step-by-step explanation:

correct choice is b

step-by-step explanation:

when you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. for the function the average rate of change from point to point can be calculated as

to find the average rate of change from day 2 to day 10, note that at day 2, 8 houses were sold, so a(2,8) and at day 10, 2 houses were sold, so b(10,2). thus,