Solving Linear equations(Substitution method)

In this definition, x is not necessarily a real number, but can in general be a member of any vector space. A less restrictive definition of linear function, not coinciding with the definition of linear map, is used in elementary mathematics.
The concept of  linear algebra tutoring online can be extended to linear operators. Important examples of linear operators include the derivative considered as a differential operator, and many constructed from it, such as del and the Laplacian. When a differential equation can be expressed in linear form, it is particularly easy to solve by breaking the equation up into smaller pieces, solving each of those pieces, and adding the solutions up.

Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (also called linear spaces), linear transformations (also called linear maps), and systems of linear equations.Let’s see an example from 7th grade math equations

Question:-

Solve the system of linear equations -2x+3y=8,3x-y=-5

Answer:-

-2x+3y = 8  ——–> 1

3x-y = -5 ——–> 2

multiply equation 2 by 3 and add it equation 1 ,this shows how to solve equations

-2x + 3y = 8

9x – 3y = -15

———————

7x    =  -7

divide both sides by 7

x = -1
substitute x = -1 in equation 2
3x – y = -5

3(-1) – y = -5

-3-y = -5

-y = -5+3

-y = -2

y = 2

So x = -1 and y = 2 is the Answer.

What is Expanded Form

Expanded form shows a number expanded into an addition statement.In simple words,we will expand the number in small parts so that ,if you add all this parts again you will get the actual number.

Here  algebra tutor have given few examples for you to understand this much better.

1) Expanded form of 485

485=400+80+5

2) Expanded form of 50545

50545=50000+500+40+5

3) Expanded form of 1 million 656 thousand

1656000=1000000+600000+50000+6000

4) Expanded form of 4.97

4.97 = 4 + 0.9 + 0.07

 The simplest way to write numbers in expanded form is to write them sort of in English.Here is an algebra question which explains this.

12,345 becomes 1 ten thousand and 2 thousands and 3 hundreds and 4 tens and 5 ones. Changing the words to math symbols, 12,345 in expanded form is:

1 x 10,000 + 2 x 1,000 + 3 x 100 + 4 x 10 + 5 x 1

 You can find more examples on elementary algebra practice problems.

 

How to find Factors for a Equation

An equation is a mathematical statement, in symbols, that two things are exactly the same (or equivalent). Equations are written with an equal sign, as in 2+3 = 5 or 9-2 = 7 . The equations above are examples of an equality: a proposition which states that two constants are equal. Equalities may be true or false.

Equations are often used to state the equality of two expressions containing one or more variable. In the reals we can say, for example, that for any given value of x it is true that

x(x-1) = x²-x.We also can find factors for the equations by using factoring calculator ,similarly we have quadratic formula calculator to find the factors of a quadratic equations.

The equation above is an example of an identity, that is, an equation that is true regardless of the values of any variables that appear in it. The following equation is not an identity:

x²-x = 0

Let’s see an example on this

Solve (2x+2)²=√16

Take square root from both sides,

2x+2 = 16

2x+2 = + or- 4

There are two possibilities

1)2x+2 = 4

subtract 2 from both sides

2x = 4-2

2x = 2

divide both sides by 2

x =1

2) 2x+2 = -4

subtract 2 from both sides

2x = -4-2

2x = -6

divide both sides by 2

x = -3

So the answer is x = 1,-3

In the same way we can find factors for linear equations in two variables.

For more solved questions and help – http://solvedmathproblems.wordpress.com/

Solution for How to do Fractions

Fractions is a part of math which is a basic operation used to simplify number of numerical expressions. Fractions can be defined as “A number which represent the part of a whole number”. There are three types of fraction as given below and examples may serve you as a good fractions help to identify fraction of different types.

1) Proper Fractions : Numerator < Denominator
Proper fractions have the nominator less than the denominator part,
for example -

  7
 ----
  25

2) Improper Fractions : Numerator > Denominator or Numerator = Denominator,
Improper fractions have the nominator greater than or equal to denominator,
for example -

  27
 -----
   5

3) Mixed Fractions : Mixed fractions have a whole number and a fraction,
for example -

    7
14 ----
    25

.

Now to how to do fractions. Here is one simplification for your practice. And also a help with equations with fractions

Question : Solve simple 2.35 and do 12 parts of 312
Solution :

2.35
    235
=  ------   [Once the decimal point is removed]
    100

and

12 part of 312 means

 312
-----
  12

    26
=  ----
    1
or
    312
=  -----
     12
    156
=  -----
     6
    78
=  ----
     3
    26
= -----
     1

Case 2: Solve equation with fraction

 2        5          6         1
----  +  ----   -   ----   =  ----
 6        10          8        12

To solve equation with fraction follow the steps,
Consider Left hand side terms of the equation

  2        5          6
----  +  -----   -   ----
  6       10          8
Need to find LCM of 6,10,8 that is 120
and multiply numerator of each term with same number
which has to be multiplied by denomenator to get LCM,
6 x 20 = 120, 10 x 12 = 120 and 8 x 15
so equation becomes ,
 2x20       5x12         6x15
------- + --------   - -------
  120        120          120

    40   +   60   -   90
=  ----------------------
              120

     100   -  90
=  ---------------
          120

   10
= -----
   120

   1
= ----   =   Right hand side.
   12

For more help with equations with fractions do contact us.

Problem on Rational expressions

We now need to look at rational expressions. A rational expression is nothing more than a fraction in which the numerator and/or the denominator are polynomials.There is an unspoken rule when dealing with rational expressions that we now need to address. When dealing with numbers we know that division by zero is not allowed. Well the same is true for rational expressions. So, when dealing with rational expressions we will always assume that whatever x is it won’t give division by zero. From linear algebra tutoring online
write these restrictions down, but we will always need to keep them in mind.

Question:-

Simplify the following rational expression

    54x2y
    ---------
    18x2y.4.x3

Answer:-
We can use the rational expression calculator ,let’s see how to solve it manually.

Factoring the numerator and denominator by using the GCF,

   18x2y.3
   --------
   18x2y.4.x3

 canceling the common factors

we get
        3
     = ----
       4x3

This is how we can evaluate the expression ,but using the calculator ,it would be much easier and we can do it on exact fractions.

How to find Perimeter of a Triangle

Perimeter of a triangle:

A perimeter is a path that surrounds an area. The word comes from the Greek peri (around) and meter (measure). The term may be used either for the path or its length. The perimeter of a circular area is called circumference.Calculating the perimeter has considerable practical applications. The perimeter can be used to calculate the length of fence required to surround a yard or garden. The perimeter of a wheel (its circumference) describes how far it will roll in one revolution. Similarly, the amount of string wound around a spool is related to the spool’s perimeter.

The circumference of a circle is the length around it. The circumference of a circle can be calculated from its diameter.we can get it by using Circumference formula

•    The sum of the measures of AB, BC and CA is called the perimeter of the triangle ABC.
•    Perimeter of triangle ABC = BC + CA + AB = a + b + c, where a, b and c are the lengths of the sides BC, CA and AB.

Let’s see a example from 8th grade math worksheets

Example:

The length of sides of a triangle are given by a = 2 cm, b = 5 cm, and c = 4 cm. Find the perimeter of the triangle formed by the lines segments BC, CA, and AB.

Answer:

Perimeter of the triangle = a + b + c = 2 + 5 + 4 = 11 cm

How to calculate simple Interest

Simple interest is calculated only on the principal amount, or on that portion of the principal amount which remains unpaid.

The amount of simple interest is calculated according to the following formula:

I= PTR/100

Where P=Principal,T= time,R=rate percent per annum

Lets see how to calculate simple interest
Question:-

If the principal is $1250 for 1 year on 2% rate of interest ,
Find the simple interest?

Answer:-

Given

p=$1250

t= 1

r= 2%

Simple interest formula is PTR/100

So by substituting the above values in the formula

We get

       1250 x 1 x 2
    I= -------------
           100

          250
      =  -----
          100

      = 25

So the simple interest is $25.
For more help on this ,you can reply me.

How to solve exponential with same base

Topic:- Exponential s with same base

The exponent is usually shown as a superscript to the right of the base. The exponentiation aⁿ can be read as: a raised to the n-th power, a raised to the power [of] n or possibly a raised to the exponent [of] n, or more briefly: a to the n-th power or a to the power [of] n, or even more briefly: a to the n. Some exponents have their own pronunciation: for example, a² is usually read as a squared and a³ as a cube

Question:-

3(9)²ⁿ=(3ⁿ⁺¹)³

Answer:-

3(9)2n=(3n+1)3

3*(32)2n=33n+3

When the bases are same ,powers can be added

34n+1=33n+3

When base is same both sides ,We can equate the powers like

4n+1 = 3n+3

subtract 3n on both sides

  4n+1 = 3n+3
    -3n  -3n
------------------
   n+1 = 3
    -1   -1
-----------------
     n = 2

So 2 is the answer.

For more help on this,you can reply me.

Problem on square roots

Topic:-square roots

a square root of a number x is a number r such that r² = x, or, in other words, a number r whose square (the result of multiplying the number by itself) is x.Adding and subtracting square roots is just like combining like terms when you need to do that with algebraic expressions

This math help is a part of  roots.

Question:-

solve √6(7√3+6)

Answer:-

√6(7√3+6)

√6(7√3)+√6(6)

7√18+6√6

7√(9*2)+6√6

7*3√2+6v6

21√2+6√6 (Answer)

For more help on roots ,you can reply me.

Example for solving Simultaneous equations

Here is an algebra question on Simultaneous equations are representations of multi-variant sets of relationships (functions) and one of the advantages of linear programming.

Topic : Simultaneous equations

There are  also simultaneous inequations like simultaneous equations where the unknown value of variables are calculated.

Problem : Solve y = x + 2 and 3x + 2y = 9

Solution :

y = x + 2 ------- (equation 1)
3x + 2y = 9 ------ (equation 2)
we have to solve this by substitution method
Lets substitute the value of y from equation 1 in equation 2

equation 2 is
3x + 2y = 9
now put y = x + 2 in this equation

3x + 2(x + 2) = 9
3x + 2x + 4 = 9
5x = 9 - 4
5x = 5
x = 5/5
x = 1

Now on substituting the value of x in equation 1 gives,
y = x + 2
y = 1 + 2
y = 3

So now x = 1 and y = 3
(1,3) is the answer

For more simultaneous problems to practice contact algebra help.