Transcript System of Equations: 0, 1, and Infinite Solutions

Solving System of Equations
that have 0, 1, and Infinite
Solutions
One Solution
Solve the following system of equation algebraically and
graphically:
Both equations equal
y. Set them equal to
each other.
2x  22  3x  28
22  5x  28
50  5x
10  x
y  2x  22
y  3 x  28
10, 2
y  3 10  28  30  28  2
The lines only intersect
once since there is one
solution.
No Solution
Solve the following system of equation algebraically and
graphically:
Add the equations to
eliminate a variable:
2 x  2 y  18
2 x  2 y  6
2 x  2 y  18
2 x  2 y  6
 _____________
0  12
No Solution.
The two lines are
parallel. They
never intersect.
Infinite Solutions
Solve the following system of equation algebraically and
graphically:
The two equations are
y  2 x  5
2 y  4 x  10
equivalent. They lie on
top of each other. They
intersect everywhere.
2  2 x  5  4 x  10
4x 10  4x  10
10  10
True
Infinite Solutions.
Every point that satisfies:
y  2 x  5
THE LINES COINCIDE