Download Notes/Math/9R Elimination Add Subtract

Systems of Equations
A system of equations is when you have two
equations with two unknown variables that
need to be solved for.
The solution to a system of equations is an
ordered pair (a point) that satisfies both
equations.
We use addition or subtraction to eliminate one
variable when the coefficients of a variable
(numbers in front of the variable) are the same.
Ex: Add the two equations together.
3x – 5y = – 16
2x + 5y = 31
Ex: Subtract the two equations.
5x + 2y = 6
9x + 2y = 22
Steps:
1) Find the variable that’s coefficients are the same or
opposites.
2) Determine whether you need to add or subtract the
equations to eliminate (cancel out) that variable.
a. SAME SIGNS SUBTRACT
b. DIFFERENT SIGNS ADD
3) Add/Subtract the equations and solve for one variable.
4) Substitute your answer into one of the equations and
solve for the other variable. (You can choose either
equation.)
Solve each system of equations using elimination
3x  5 y  3
4x  5 y  4
2x + 4y = 30
– 2x – 2y = – 18
On Your Own:
3x  2 y  4
4 x  2 y  10
Solve each system of equations using elimination
x  3y  5
x  2 y  10
Use elimination to solve the system of equations.
Answer: (2, 1)
– 4m + 2n = 6
– 4m + n = 8
5s + 2t = 6
9s + 2t = 22