Solving System of Equations

In mathematics, a system of linear equations is a collection of linear equations involving the same set of variables. For example,

is a system of three equations in the three variables . A solution to a linear system is an assignment of numbers to the variables such that all the equations are simultaneously satisfied. A solution to the system above is given by

since it makes all three equations valid.so this is specially for linear equations in two variables or more than two variables.

In mathematics, the theory of linear systems is a branch of linear algebra, a subject which is fundamental to modern mathematics. Computational algorithms for finding the solutions are an important part of numerical linear algebra, and such methods play a prominent role in engineering, physics, chemistry, computer science, and economics. A system of non-linear equations can often be approximated by a linear system (see linearization), a helpful technique when making a mathematical model or computer simulation of a relatively complex system.This is how linear equations explained ,let's see a example on this now from linear algebra tutoring online.
Question:-

Solve the system of equations

8x-z=4

y+z=5

11x+y=15

Answer:-

8x-z=4 ----- eq1

y+z=5 ---- eq2

11x+y=15 -----eq3

add eq1 and eq2

we get 8x+y=9 ----- eq4

subtract eq4 from eq3

11x+y=15
-8x+y=9
-----------
3x = 6

x =2

putting this value in eq1

8x-z =4

16-z=4

z=12

putting this value in eq2

y+z = 5

y = -7

so x=2 , y= -7 and z=12

Commutative and Distributive Number Properties

Number properties are
Associative property applies to both addition and multiplication: a+(b+c)=(a+b)+c, a*(b*c)=(a*b)*c.
Distributive property ties addition and multiplication together. Distributive property can be written as: a*(b+c) = a*b + a*c.
Commutative property means that operands can switch places: a+b=b+a, a*b=b*a.

For Example:
Question 1 :- Distributive PropertyThe property demonstrated in the equation -(3n - 5) = -3n + 5 is:
a. associative b. commutative c. distributive d. Neither side of the equation is equal to the other.
Answer:
-1(3n-5) = -3n+5
(-1) (3n) + (-1) (-5)
= -3n+5 (Distributive Property)

Question 2 :- Associative Property
property demonstrated in the equation (5 + n) - 2 = 5 + (n - 2) is:
Answer:
(5+n)-2 = 5+(n-2)
Here the grouping that is the parentheses has changed.so it a (Associative Property)

Question 3 :- Commutative Property
property is this one 7 - 4 + 2 = 7 + 2 – 4
Answer:
7 - 4 + 2 . 7 + 2 - 4
Here the order - 4 + 2 has become 2 + - 4. So it is a (Commutative Property)

problem on elimination methos

Topic:- Elimination method

When we are solving equations in algebra ,We can add or subtract the equations ,So that
We can simplify the equations , This is called elimination method

Here we have a simple example to show you ,how this methos works.

This algebra help shows ,how to solve equations as well.

Question :

x+y = 7 and x-y = 9

Solve for 'x',By using elimination method.

Answer:-

Let's add both the equations

      x + y = 7
      x - y = 9
 ------------------
        2x = 16


Divide with 2 on both sides


       2x     16
      ---- = -----
       2       2


        x = 8


So 8 is the answer


For more help ,please reply me .

Converting an algebraic expression into dependent variables of a single variable

Here is an algebra question where in a given algebraic expression like terms are on one side and unlike term on another side, this problem is all about making into different subject.

Topic : Making into different subject

This example would clearly explain what making into different subject exactly mean.

Problem : Let f = uv / (u + v) Make “v” as the subject

Solution :

f = uv / (u + v)
Multiplying by (u + v) on either sides of the equation
f (u + v) = uv
fu + fv = uv
Subtract fv on both the sides
fu = uv – fv
fu = v(u – f)
fu / (u – f) = v

Hope the meaning on coverting to different subject is well understood by above example, for more algebra questions like this contact algebra help.