Download Solving Linear Systems Algebraically

Solving Linear Systems Algebraically
Section 3-2
Steps in Elimination
AKA: “Linear Combination”
 Steps:
1.
2.
3.
4.
ARRANGE equations in like terms and
multiply a term to attempt to cancel out a
variable
ADD the variables where at least one variable
cancels out
REPLACE the value into either equation
CHECK the solution
Example 1

Solve using Elimination
2 x  7 y  10

 x  3 y  3
2 x  7 y  10

(2) x  3 y  3
2 x  7 y  10
2 x  6 y  6
y4
Example 1
 Solve
using Elimination
2 x  7 y  10

 x  3 y  3
2 x  7 y  10

 x  3 y  3
y4
2 x  7(4)  10
2 x  28  10
2 x  18
x9
(9, 4)
Example 1
 Solve
using Elimination
2 x  7 y  10

 x  3 y  3
(9, 4)
2(9)  7(4)  18  28  10  10

(9)  3(4)  9  12  3  3
Example 2
 Solve
(2)
(3)
using Elimination
3 x  11 y  4

2 x  6 y  0
3 x  11 y  4

2 x  6 y  0
3 x  11 y  4
3 x  11(2)  4
3 x  18
x  6
6 x  22 y  8

6 x  18 y  0
4y  8
y2
( 6, 2)
Example 2
 Solve
using Elimination
3 x  11 y  4

2 x  6 y  0
( 6, 2)
4. CHECK the solution
3( 6)  11(2)  18  22  4  4

2( 6)  6(2)  12  12  0  0
Your Turn
 Solve
using Elimination
x  6 y  1

3 x  5 y  10
(-3) x  6 y  1

3 x  5 y  10
( 5,1)
5/24/2017 1:57 AM
3x  18 y  3 x  6(1)  1
3x  5 y  10
x  6 1
13 y  13 x  5
y 1
3-2 - Solving Systems through Substitution
Three pizzas and four sandwiches cost $34. Three
pizzas and seven sandwiches cost $41.50.
How much does a pizza cost? How much does a
sandwich cost?
3 x  4 y   34
Let x = pizza
(-1) 3 x  4 y  34
Let y = sandwich
3x  4  2.5  34
3 x  10  34
3 x  24
x8
3x  7 y  41.5
3x  7 y  41.5
3 y  7.5
Pizza cost $8
Sandwich cost $2.50
y  2.5
Sally has $21.40 in dimes and quarters, for a total of
100 coins.
How many of each kind of coin does Sally have?
Let d= dimes
Let q = quarters
d  76  100
d  24
(-10) d  q  100
10d  25q  2140
10d  10q   1000
10d  25q  2140
15q  1140
24 dimes
76 quarters
q  76
Assignment

Page 194 (6-9, 19, 20)
 Write the Problem!!!
 Show ALL WORK—STEPS
 Be NEAT