5.1 SOLVE SYSTEMS BY GRAPHING
A system of equations
is two (or more) equations paired
together that use the same
variables.
Example:
These equations are paired
together, and both use the same
variables (x and y).
5x – 4y = 8
–2x + 7y = –11
The solution to a system is the one
"special" ordered pair that works in
both or all equations in the system.
Testing Possible Solutions
To test a solution, plug the ordered
pair into BOTH equations.
If it works in BOTH, then it IS A SOLUTION for the system.
Example:
Is (4, 1) a solution to the system?
x + 2y = 6
pull
3x + y = 11
slope-intercept
b
y
m
rising
falling
intersect
ordered
2y = 3x – 4
pair
4y + x = 20
CHECK YOUR SOLUTION
2y = 3x – 4
4y + x = 20
5.1 SOLVE SYSTEMS BY GRAPHING
2y = 4x – 6
y – 5x = –9
CHECK YOUR SOLUTION
2y = 4x – 6
y – 5x = –9
solution:
(2, 1)
3y = 4x + 3
y = 4/3x + 1
3y = –2x – 15
y = -2/3x - 5
CHECK YOUR SOLUTION
3y = 4x + 3
solution:
(-3, -3)
3y = –2x – 15