Download 7-3: Solving Systems Using Elimination

Section 5.3: Solving Systems Using Elimination Notes
POD: Solve the system by substitution.
2.) 2x – 3y = -1
y=x-1
(4, 3)
Objective: Students will be able to solve systems using the elimination method. Students will be
able to discuss the difference between elimination and substitution methods of solving systems.
How to Solve a System Using Elimination:
1.) Multiply one equation in order to get coefficients that have a sum or difference of zero
(Use the LCM!!)
2.) Add the equations to eliminate one of the variables
3.) Solve for the variable
4.) Plug in the value you got from step 3 into either equation
5.) Solve for the other variable
Examples
1.)
5x – 6y = -32
3x + 6y = 48
8x
8
x
= 16
8
=2
2.) -4x +9y = 9
x -3y = -6
5(2) -6y = -32
10 + -6y =-32
-10
-10
-6y = -42
-6
-6
y=7
-4x + 9y = 9
4(x – 3y = -6)
(2, 7)
-4x + 9y = 9
4x – 12y = -24
-3y = -15
-3
-3
x -3(5) = -6
x – 15 = -6
x=9
(9, 5)
y =5
3.) 16x – 10y = 10
-8x -6y = 6
-8x – 6(-1) = 6
-8x +6 = 6
-8x = 0
x=0
4.) 3x - 7y = 16
-9x + 5y = 16
-3x + 7(-4) = -16
-3x – 28 = -16
-3x = 12
x = -4
16x – 10y = 10
2(-8x – 6y = 6)
16x -10y = 10
-16x -12y = 12
-22y = 22
-22 -22
y = -1
(0, -1)
3(3x + 7y = 16)
-9x + 5y = 16
9x – 21y = 48
-9x + 5y = 16
-16y = 64
-16
-16
y = -4
(-4, -4)