Transcript 8-3 Addition method AKA Combination or Elimination

8-3 Addition method
AKA Combination or Elimination
9P9: Solve 2X2 systems by elimination
Steps
1)
2)
3)
4)
5)
6)
7)
Put both into standard form (Ax+By =C) and stack
Multiply 1 (or both) equation(s) to make opposites
Add (combine) the equations (one var is eliminated)
Solve for the remaining variable
Put that value in (either equation) solve for other
variable
Write solution as ordered pair
Check
Example 1
Remember to solve for
second variable
You can use either equation!
x+y=5
+ 2x - y = 4
3x
3
=9
3
x =3
3+y=5
-3
-3
y=2
The solution is
(3,2)
Example 2
7x – 5y = 76
( 4x + y = 55 )5
We need opposites here.
7x – 5y = 76
+ 20x + 5y = 275
4(13) + y = 55
27x
52 + y = 55
27
y=3
The solution is
(13,3)
= 351
x = 13
27
Example 3
( 2x + 3y = 20 )3
( 3x + 5y = 37 )-2
Here we need to change both
equations
By making x’s 6 or y’s 15
6x + 9y = 60
+ -6x -10y = -74
2x + 3(14) = 20
2x + 42 = 20
2x = -22
x = -11
The solutions is (-11,14)
-1y = -14
y = 14
Which method would you use?
Why?
y = 2x – 6
3x = 3y -6
Write a system to solve
The difference between two numbers is 36. One sixth of
the larger number minus one ninth of the smaller number is
11. Find the numbers.
To get rid of fractions
use the LCD
N1: x
N2: y
( x - y = 36 )-3
-3x + 3y = -108
( 1 x  1 y  11)18
6
9
+ 3x - 2y = 198
x – 90 =36
x = 126
The numbers are 126 and 90
y = 90
assignment

8-3/ 371/ 1-12
Assignment


8-3/371/15-39 odd, 50-58 even
Quiz tomorrow 8-1 to 8-3