Transcript The Elimination Method

Solving a System of Equations
with the Elimination Method
The Elimination Method
2 x  3 y  2
+
+
5 x  3 y  16
+
+
Combine these two mats into one mat
=
–
=
–
–
–
The Elimination Method
+
2 x  3 y  2
 5 x  3 y  16
+
7 x  14
7
x2
2  2   3 y  2
4  3 y  2
=
4
4
3 y  6
3
–
CHECKS:
2  2  3  2  2
7
–
5  2  3  2  16
3
y  2
 2, 2
Elimination Method
Solve the following system of equation:
2 x  y  2
2 x  3 y  10
Add the equations to
eliminate a variable:
2 x  y  2
2 x  3 y  10
 _____________
2y  8
2
2
y4
Check in both Equations:
2 1  4  2
Solve the other
variable:
2x 44  42
2x  2
2 2
x 1
1, 4
Answer the
question:
2 1  3  4   10
Elimination Method
Solve the following system of equation:
3x  4 y  1
 2 x  4 y  2   1
In order to add, there must
be opposites to eliminate.
Add the equations to
eliminate a variable:
3x  4 y  1
2 x  4 y   2
 _____________
x  1
 1,1
Solve the other
variable:
3  1  4 y  1
3  4 y  1
3
Answer the
question:
Check in both Equations:
3  1  4 1  1
3
4y  4
4
4
y 1
2  1  4 1  2
Adding and Subtracting Fractions
Subtraction:
Addition:
2
3
2
3

1
5
  
5
5
10
15
1
5

13
15
3
15
3
3
Common
Denominator
Add the
Numerators
7
4
7
4

3
10
  
5
5
35
20

29
20
Least
Common
Denominator
(if you can
find it)
3 2
10 2
6
20 Subtract the
Numerators
Elimination Method
Solve the following system of equation:
Pick a variable to eliminate:
x
y
4 x  3 y  10
9x  4 y  1
The Elimination Method is similar to
adding/subtracting fractions, except that you
want opposites. The goal is to multiply
equations, if needed, so the coefficients (the
number before a variable) for one of the
variables is opposite of the other.
Elimination Method
Solve the following system of equation:
Sometimes you need
to multiply BOTH
equations to have
opposite coefficients
on the same variable
 4 x  3 y  10   9
 9 x  4 y  1  4
4
x

3
2

10


36 x  27 y  90
4x  6  10
6
6
36 x  16 y  4
 ______________
4x  4
43 y  86
4 4
43
43
x

1
1, 2 

y2
Add the equations to
eliminate a variable
Solve for
the other
variable
Check in both Equations:
4 1  3  2  10
9 1  4  2  1
Answer the
question
Elimination Method
Solve the following system of equation:
Pick a variable to eliminate:
x
y
4 x  3 y  10
9x  4 y  1
Now solve the problem
by eliminating the other
variable.
The Elimination Method is similar to
adding/subtracting fractions, except that you
want opposites. The goal is to multiply
equations, if needed, so the coefficients (the
number before a variable) for one of the
variables is opposite of the other.
Elimination Method
Solve the following system of equation:
Sometimes you need
to multiply BOTH
equations to have
opposite coefficients
on the same variable
 4 x  3 y  10   4
9 x  4 y  1  3
4
1

3
y

10


16 x  12 y  40
4  3 y  10
4
4
27 x  12 y  3
 ______________
3y  6
43x  43
3 3
43
43
y2
1,
2


x 1
Add the equations to
eliminate a variable
Solve for
the other
variable
Check in both Equations:
4 1  3  2  10
9 1  4  2  1
Answer the
question