What values do x and y have if |x| = 16, and when x and y are combined they equal 0?

Answer 1

Hi Jaelyn, I cant take a stab at this problem.

So, we want the absolute value of x to equal 16, and we want x + y to equal 0.

1. Since the absolute value of a number is its distance form 0 on the number line, this means we can have x be either 16 or -16. Notice how the absolute value of 16 is 16 and the absolute value of -16 is 16. We are done here.
2. The equation x + y = 0 states that the sum of x and y is 0. From our previous equation, we have x can be either -16 or 16. Plug both these values into the equation x + y = 0 to find corresponding y-values. When we plug x = -16 into the equation x + y = 0, we get y = 16 and when we plug x = 16 into the equation x + y = 0, we get y = -16.

So, there are two possible pairs of values for x and y that satisfy both of our equations. They are (-16, 16) and (16, -16). A good way of checking your work would be to plug these values in for x and y, and see if the equations equate.

For example, for our pair (-16, 16), see that the absolute value of -16 is 16 and that -16 + 16 equals 0. I will leave it up to you to check that our pair of solutions (16, -16) is in fact a solution. I hope that was helpful!