Important Steps and Information
The operation used to combine two linear equations in a system to eliminate one variable.
Addition (line up equations and add to eliminate first variable, x or y)
Solve the following system of equations by elimination:
5x + y = -25
-5x + y = 25
(-5, 0)
Solve the following system of equations by elimination:
-x + y = 9
-5x - y = 21
(-5, 4)
Solve the following system of equations by elimination:
-2x + 4y = -22
6x - y = 22
(3, -4)
Solve the following system of equations by elimination:
–9x − 4y = –12
–3x + y = –18
(4, -6)
To eliminate a variable, the two like terms you're adding must have WHAT?
Opposite Coefficients
Solve the following system of equations by elimination:
-4x - y = 5
2x + y = -1
(-2, 3)
Solve the following system of equations by elimination:
9x + 8y = –1
7x + 8y = 17
(-9, 10)
Solve the following system of equations by elimination:
-6x - 2y = 16
7x + 6y = 18
(-6, 10)
Solve the following system of equations by elimination:
-2x + 5y = 15
-5x - 15y = -100
(5, 5)
No matter the solution method, this final step is crucial when solving any system of linear equations before moving on to another problem.
Checking your answer
(Substituting ordered pair, calculator check, mental math, etc.)
Solve the following system of equations by elimination:
-3x - 3y = 6
5x + 3y = 0
(3, -5)
Solve the following system of equations by elimination:
–4x − 3y = 11
–4x − 6y = 14
(-2, -1)
Solve the following system of equations by elimination:
-7x + 9y = 18
-5x + 3y = -18
(9, 9)
Solve the following system of equations by elimination:
-7x - 7y = 63
-21x - 21y = 189
ALL REAL NUMBERS (ℝ)
When multiplying one of the equations in a system to create opposites to cancel one of the variables, what is a key thing to remember during this step?
You must multiply EVERY term of the equation by the constant multiplier
Solve the following system of equations by elimination:
2x + 2y = 10
-2x - 4y = -18
(1, 4)
Solve the following system of equations by elimination:
–4x − y = 15
5x − y = –3
(-2, -7)
Solve the following system of equations by elimination:
-5x - 4y = -42
35x - 6y = 192
(6, 3)
Solve the following system of equations by elimination:
-7x - 3y = 24
-35x - 15y = 6
NO SOLUTION (∅)