Question

13. Solve the following system by any method. 8x + 9y = –5 –8x – 9y = 5

Answer 1

Just add the like terms together.

Answer 2

Answer: the system is indeterminate and has infinite solutions.

Justification.

1) System:

Given:

  8x + 9y = –5
–8x – 9y = 5

2) I will show you that system is not determined:

Add the two equations:

8x - 8x + 9y - 9y = - 5 + 5

0 = 0

3) You have gotten an identity which is true for all x, meaning that there are infinite solutions.

So, the answer is that the system is indeterminate and has infinite solutions.

Do you know why does that happen?

It is because the two equations are equivalent, meaning that they are the same line.

You can prove that the two equations are equivalent by multiplying any of them by -1, which will turn one equation into the other.

For example, multiply 8x + 9y = - 5 times - 1:

=> - 8x - 9y = 5,which is the second equation.