# Algebra

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

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1. 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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