The given system of equations is:
x + y = -9
-x - y = 9
Adding the two equations together will give:
0 = 0
This implies that the two equations are dependent on each other and represent the same line. Therefore, the system of equations has infinitely many solutions due to this dependency.
how many solutions does the system of equations have? x + y = -9 and -x -y = 9
3 answers
can you show how to add them?
Certainly! To add the two equations together, we will perform the following steps:
x + y = -9
-x - y = 9
_____________
0 = 0
When we vertically add the two equations together, each term is added separately:
(x + y) + (-x - y) = -9 + 9
Simplify the left side:
x + y - x - y = 0
Combine like terms:
0 = 0
This final equation shows that the two original equations sum up to zero. Since they add up to zero, this suggests that the two equations are dependent on each other and have infinitely many solutions.
x + y = -9
-x - y = 9
_____________
0 = 0
When we vertically add the two equations together, each term is added separately:
(x + y) + (-x - y) = -9 + 9
Simplify the left side:
x + y - x - y = 0
Combine like terms:
0 = 0
This final equation shows that the two original equations sum up to zero. Since they add up to zero, this suggests that the two equations are dependent on each other and have infinitely many solutions.
1 answer