Solution to a system
The ordered pair (or set of points) that satisfy all equations in the system, at the same time
Called the point of intersection
There are three different types: no solution, infinite solutions, one solution
One Solution
The two lines cross each other in exactly one point on the graph
Infinite Solutions
The two lines on the graph lie on top of each other.
No Solution
The two lines never cross.a = b
x = a
a = a
QuestionsHow many times do the lines cross in order to have one solution?
What does having a solution mean?
What does every line need to have when drawn?
Guided Practice 4Find the solution to given system:
x – y = 4-5x + 5y = -20
x – y = 4-x -x -y = -x + 4__
-1__-1
__-1
y = x - 4
-5x + 5y = -20+5x +5x____________
5y = 5x – 20 __ 5
__ 5
__ 5
y = x – 4
y = x - 4 y = x – 4
Solution:Infinite Solutions
Guided Practice 5Find the solution to given system:
-4x + 8y = 16 6x – 3y = 12
-4x + 8y = 16+ 4x + 4x______________ 8y = 4x + 16__
8__ 8
__ 8
y = 1x + 2 2
y = 1x + 2 2
-6x -6x____________-3y = -6x + 12__-3
__-3
__-3
y = 2x – 4
y = -2x – 4
Solution:(4, 4)
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