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Title: Algebra _ Simultaneous Equations
Description: Algebra _ Simultaneous Equations The simultaneous equation is an equation that involves two or more quantities that are related using two or more equations. It includes a set of few independent equations. The simultaneous equations are also known as the system of equations, in which it consists of a finite set of equations for which the common solution is sought. To solve the equations, we need to find the values of the variables included in these equations. The system of equations or simultaneous equations can be classified as: Simultaneous linear equations (Or) System of linear equations Simultaneous non-linear equations System of bilinear equations Simultaneous polynomial equations System of differential equations.
Description: Algebra _ Simultaneous Equations The simultaneous equation is an equation that involves two or more quantities that are related using two or more equations. It includes a set of few independent equations. The simultaneous equations are also known as the system of equations, in which it consists of a finite set of equations for which the common solution is sought. To solve the equations, we need to find the values of the variables included in these equations. The system of equations or simultaneous equations can be classified as: Simultaneous linear equations (Or) System of linear equations Simultaneous non-linear equations System of bilinear equations Simultaneous polynomial equations System of differential equations.
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Algebra
Simultaneous Equations
1
...
Solve 3x – 2y + z = 2, 2x + 3y – z = 5, x + y + z = 6
Solution:
3x – 2y + z = 2
-----(1)
2x + 3y – z = 5
-----(2)
x+y +z
= 6
(1)
3x – 2y + z
= 2
(2)
2x + 3y – z
= 5
add
5x + y
= 7
(2)
2x + 3y – z
= 5
(3)
x+y+z
= 6
3x + 4y
= 11
(4) x 4
20x + 4y
= 28
3x + 4y
= 11
17x
= 17
x
= 1
(5)
Subt
...
Solve x + 2y + z = 7, x + 3z = 11, 2x – 3y = 1
Solution:
x + 2y + z
=
7
-------(1)
x + 3z = 11
-------(2)
2x – 3y = 1
-------(3)
(1) x 3
3x + 6y + 3z = 21
x + 3z = 11
(3)
(3)
Subtract,
2x + 6y = 10
2x – 3y = 1
Subtract
from (4)
from (1),
9y
= 9
y
= 1
2x + 6
= 10
2x
= 4
x
= 2
2+2+z = 7
z
= 3
Solution is x = 2, y = 1, z = 3
------(4)
4
...
z = 10
Solve 3x – 4y = 6z – 16, 4x – y – z = 5, x = 3y + 2 (z – 1)
Solution:
= 16
------(1)
=
5
------(2)
x – 3y – 2z
= 2
------(3)
3x – 4y – 6z
= 16
24x – 6y – 6z
= 30
3x – 4y – 6z
4x – y – z
(1)
(2) x 6
Sub,
(2)x 2
(3)
Sub
21x + 2y
= 46
8x – 2y – 2z
= 10
x – 3y – 2z
= 2
7x + y
= 12
(4) 21x + 2y
= 46
(5) x 2
x + 2y
= 24
35x
= 70
Sub,
x
=
2
-----(4)
-----(5)
from (5)
14 + y = 12
= 2
y
from (2)
8+2–z
=
5
z
=
5
Solution is x = 2, y = 2, z = 5
6
...
Solve
1
2
+ 4 = 0,
x
y
Solution:
1
y
1
z + 1 = 0,
1
x =a,
1
= b,
y
1
= c
z
(2) x 2
(3)
a – 2b
b–c
2c + 3a
2b – 2c
2c + 3a
=
=
=
=
=
Add
(1)
3a + 2b
a – 2b
= 12
= 4
Add
From (1)
From (2)
4a
a
2 – 2b
2b
b
3–c
c
c
=
=
=
=
=
=
=
=
4
1
14
2
14
8
2
4
6
3
1
4
4
Subtract is a = 2, b = 3, c = 4
1
i
...
x = 2 ,
y =
1
1
, z = 4
3
2
z
3
+ = 14
x
-----(1)
-----(2)
-----(3)
9
...
e x =
1
2z = 20
1
z = c
= b,
a + b + c = 36
a + 3b – c = 28
a +
1
1
+
x
3y +
1
,
8
y =
1 , z = 1
16
12
-----(4)
-----(5)
10
...
Solve
1 ( x + y – 5) = y – z = 2x – 11 = 9 – (x + 2z)
3
Solution:
x + y – 5 = 3y – 3z
x – 2y + 3z = 5
----(1)
y – z = 2x – 11
(1)
(2) x 2
2x –11
= 9 – x – 2z
3x + 2z
= 20
(4) x 2
Sub
– 6x + 2z = – 34
3x + 2z = 20
– 9x = – 54
–18 + z
z
from (2)
----(3)
4x – 2y + 2z = 22
x
from (4)
----(2)
x – 2y + 3z = 5
– 3x + z = – 17
Sub
(3)
2x – y + z = 11
12 – y + 1
y
= 6
= – 17
= 1
= 11
= 2
Solution is x = 6, y = 2, z = 1
----(4)
12
Title: Algebra _ Simultaneous Equations
Description: Algebra _ Simultaneous Equations The simultaneous equation is an equation that involves two or more quantities that are related using two or more equations. It includes a set of few independent equations. The simultaneous equations are also known as the system of equations, in which it consists of a finite set of equations for which the common solution is sought. To solve the equations, we need to find the values of the variables included in these equations. The system of equations or simultaneous equations can be classified as: Simultaneous linear equations (Or) System of linear equations Simultaneous non-linear equations System of bilinear equations Simultaneous polynomial equations System of differential equations.
Description: Algebra _ Simultaneous Equations The simultaneous equation is an equation that involves two or more quantities that are related using two or more equations. It includes a set of few independent equations. The simultaneous equations are also known as the system of equations, in which it consists of a finite set of equations for which the common solution is sought. To solve the equations, we need to find the values of the variables included in these equations. The system of equations or simultaneous equations can be classified as: Simultaneous linear equations (Or) System of linear equations Simultaneous non-linear equations System of bilinear equations Simultaneous polynomial equations System of differential equations.