Posted by **Logan** on Monday, March 14, 2011 at 7:07pm.

When solving a system of equations by the addition method, how do you know when the system has no solution?

- Algebra -
**Henry**, Tuesday, March 15, 2011 at 11:31pm
The solution to a system of Eqs is the point where they intersect. If the 2

lines have equal slopes, they are parallel and do not intersect. Therefore, there are no solutions.

If the 2 Eqs are identical, they represent the same line and there are

infinite solutions.

Example:

Eq1: 4X + 2Y = 8.

Eq2: 2X + Y = 4.

Eq1 and Eq2 are identical. You can prove it by dividing both sides of Eq1

by 2. If you graphed the Eqs, you will

get a single line.

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