Objective - To solve a system of linear equations
using linear combinations (Elimination).
Graphic Method
Algebraic Approaches
Substitution
solution
If a = b, and b = c
then a = c.
Elimination
- Time consuming
- Not always accurate
If
a=b
and
c=d
then a + c = b + d.
Solve using elimination.
2x
y
6
3x
y
4
2x
3x
y
y
5x
5
x
6
4
10
5
2
Solution is
2x
2 2
4
4
(2,2)
y
6
y
6
y
6
4
y
2
Check!
Solve using elimination.
x
x
3y
5
y
3
x 3y
x y
5
3
4y
8
4
4
y
x
x
3y
3 2
x
2
Solution is
( 1, 2)
5
5
6
6
5
6
x
1
Check!
Solve using elimination.
y
3x
4
2x
y
5
y
3x
4
3x
y
4
y
5
2x
y
5
x
9
x
9
2x
y
3x
y
3
1
4
9
y
27
y
23
4
x
1
9
4
Solution is
( 9, 23)
Check!
Solve using elimination.
2x
x
3y
4y
4
9
2x
3y
x
4y
9
y
5
3x
4
Solve using elimination.
2x
x
3y
4y
4
9
2x
3y
2(x
4y
x
x
4
4y
4( 2)
x
9)
9
2x
3y
4
2x
8y
18
11y
11
22
11
y
9
8
9
x
1
Solution is
2
(1, 2)
Check!
Solve using elimination.
2x
5y
2x
y
10
7
2x
5y
10
5(2x
y
7)
2x
15
2
4
7
1
2
y
7
y
7
y
7
1
y
2
2x
5y
10
10 x
5y
35
12 x
12
45
12
x
S o lu tio n is
45
15
12
4
3 1
3 ,
4 2
Check!
Solve using elimination.
2x
5x
3y
5
2y
4
5( 2x 3y 5)
2(5x 2 y 4)
5x
5x
2y
2 3
5x
10 x
10 x
4
4
6
6
4
6
5x
10
x
2
15 y
25
4y
8
11y
11
33
11
y
Solution is
3
2, 3
Check!