Name ____________________
Date____________
Solving Systems by Elimination
Elimination by Addition
Before Adding make sure
“x” terms are lined up, “y”
terms are lined up, the
equal sign is lined up, AND
the constant values are
lined up.
Add Vertically
Add Down
X
Y = Constant
x + y = -1
3x - y = 5
The “y” values eliminate after adding the
equations because the coefficients of “y”
are the additive inverse of each other
x = _______
Solve for x
____ + y = -1
substitute x into the first equation to solve for y
y = ______
Solve for y
State the solution: (
Check the solution in BOTH EQUATIONS
x + y = -1
,
)
3x - y = 5
Conclusion: Your solution is correct if it checks to be TRUE in both equations
Elimination by Addition
Before Adding make sure
“x” terms are lined up, “y”
terms are lined up, the
equal sign is lined up, AND
the constant values are
lined up.
Add V_____________
Add Down
X
Y = Constant
2x + 5 y = 17
6x - 5y = -9
The “y” values eliminate after adding the
equations because the coefficients of “y”
are the additive inverse of each other
x = _______
Solve for x
2(_______) + 5y = 17
substitute x into the first equation to solve for y
y = ______
Solve for y
State the solution: (
Check the solution in BOTH EQUATIONS
Equation #1
,
)
Equation #2
Conclusion: Your solution is correct if it checks to be TRUE in both equations
Word Problem 1
Two Runways at an airport, Runway A and Runway B, have a combined length of 2,050 feet.
The difference of their length is 5,500 feet. What is the length of each runway?
Subject 1
Subject 2
Total (what does it
represent?)
What is the length of
each?
(can they be the same?)
How can you represent
the combined length?
Combined length
How can you represent
the difference of their
lengths?
Difference in length
Equation 1: ______________________________
Eliminate a variable by
ADDING the equations
together and SOLVE for
the variable that is left.
Equation 2: _______________________________
x = _______
substitute in first equation to solve for y
y = ______
solution: (
Check solution in each equation
)