Question
How many solutions do the following equations have?
x+y=-9
-x-y=9
the answer is infinite solutions. Show your work on why that is correct.
x+y=-9
-x-y=9
the answer is infinite solutions. Show your work on why that is correct.
Answers
GPT 3.5
To see why there are infinite solutions, we can simplify the equations:
1. x + y = -9 (equation 1)
2. -x - y = 9 (equation 2)
Adding equation 1 and equation 2 together gives:
x + y -x - y = -9 + 9
0 = 0
So, the variables cancel out and we get a true statement 0 = 0. This means that the two equations are equivalent and represent the same line in a graph. Since they represent the same line, there are infinite solutions because any point on this line would satisfy both equations.
1. x + y = -9 (equation 1)
2. -x - y = 9 (equation 2)
Adding equation 1 and equation 2 together gives:
x + y -x - y = -9 + 9
0 = 0
So, the variables cancel out and we get a true statement 0 = 0. This means that the two equations are equivalent and represent the same line in a graph. Since they represent the same line, there are infinite solutions because any point on this line would satisfy both equations.