7.1 solving systems of equations
DESCRIPTION
7.1 Solving Systems of Equations. Substitution Method Elimination Method. Substitution method. Given as many equations as variables. Substitution method. Given as many equations as variables. Substitution method. Given as many equations as variables. Substitution method. - PowerPoint PPT PresentationTRANSCRIPT
7.1 Solving Systems of Equations
Substitution Method
Elimination Method
Substitution method
Given as many equations as variables
1052
204
yx
yx yx 420
Substitute
10
303
105840
1054202
y
y
yy
yy
20
10420
x
x
Substitution method
Given as many equations as variables
1052
204
yx
yx
Substitution method
Given as many equations as variables
1052
204
yx
yx yx 420
Substitute
10
303
105840
1054202
y
y
yy
yy
Substitution method
Given as many equations as variables
1052
204
yx
yx yx 420
Substitute
10
303
105840
1054202
y
y
yy
yy
20
10420
x
x
10,20
Elimination Method
Given the Equations
1052
4082
yx
yx
Elimination Method
Given the Equations
1052
4082
yx
yx
1052
4082
yx
yx1 byMultiply
Elimination Method
Given the Equations
1052
4082
yx
yx
1052
4082
yx
yx1 byMultiply
10
303
y
y
Elimination Method
Given the Equations
1052
4082
yx
yx
1052
4082
yx
yx
20
2040
20104
x
x
x
1 byMultiply
10
303
y
y
Substitute
Elimination Method
Given the Equations
1052
4082
yx
yx
1052
4082
yx
yx
20
2040
20104
x
x
x
1 byMultiply
10
303
y
y
Substitute
10,20
Linear equations
The intersection of two lines is one and only one point, unless the lines are parallel or the same line.
2
4
1,32
4
xy
xy
yx
yx
What is the Solution(s) if the lines are
Parallel lines not meet, so no solution
The Same line or lines that are onto, meet at all points on the lines, Infinitely many solutions.
Solve
Find the Solutions
yxyx
yx
2
2
02
0
Solve Find the Solutions
2
020
02
02
02
0
2
2
2
x
xx
xx
xx
yxyx
yx
Solve Find the Solutions
2
020
02
02
02
0
2
2
2
x
xx
xx
xx
yxyx
yx
4,20,0
20 22
yy
Solve
Find all the values
2
24
1
12
xy
xxy
Solve
Find all the values
2
24
1
12
xy
xxy
1 ,1,0
110
10
00
121
2
22
24
242
x
xxx
xx
xx
xxx
SolveFind all the values
2
24
1
12
xy
xxy
1 ,1,0
110
10
00
121
2
22
24
242
x
xxx
xx
xx
xxx 1,0
0
01 2
y
y
)0,1(
0
11
11 2
y
y
y
0,1
0
11
11 2
y
y
y
Homework
Page 483
# 4, 12, 20, 28,
36, 44, 52, 60,
72, 78, 86, 96
Homework
Page 483
# 8, 16, 24, 32,
40, 48, 56, 68,
82, 90