Question

Describe whether the points

(−5,0),(−4,−1/2),(−3,1),(−2,3/2),(−1,2),and(0,5/2) are the set of all solutions for the equation 3x−6y=−15.

a) Yes, all of the points are solutions.
b) No, none of the points are solutions.
c) Some of the points are solutions, and some are not.
d) Can't be determined from the information given.

Answer 1

The points (-5,0), (-4,-1/2), (-3,1), (-2,3/2), (-1,2), and (0,5/2) are all solutions for the equation 3x - 6y = -15.

Step-by-step explanation:

The points (-5,0), (-4,-1/2), (-3,1), (-2,3/2), (-1,2), and (0,5/2) are the set of all solutions for the equation 3x - 6y = -15. To check this, we substitute the x and y values from each point into the equation and see if the equation holds true.

For example, if we substitute x = -5 and y = 0 into the equation, we get: 3(-5) - 6(0) = -15. This is true, so (-5,0) is a solution.

We can repeat this process for each point and verify that all the points satisfy the equation. Therefore, the correct answer is: a) Yes, all of the points are solutions.