The greatest common factor is the greatest common number if we factorize the two different numbers and multiply them respectively. Therefore after factorizing, the biggest common number between them is the greatest common factor. In other words, the greatest common factor is also known as the highest common factor which is signified by H.C.F.
Therefore the procedure goes like this if we factories the number if the two numbers are 10 and 25
Step1-divide the number 10 by 2, and you will get 5 and further divide the number 5 with five till you get 1. Therefore the factors are 2*5*1
Step 2-divide the number 25 by 5, if we factories the number then it will be 5 and five will be further divided by the number 5 and we get 1. Therefore the factors are 5*5*1
Step 3- between the factors 2*5*1 and 5*5*1, the greatest number in common is 5 and thus is called as the greatest common factor.
Step 4-Therefore 5 is the greatest common factor or is also known as the HCF or highest common factor.
Linear equations- A linear equation is in such a way because a plane is divided into two parts, the X-axis and the Y-axis. If we wish to identify a line regarding mathematics, then we need two variables and a constant and thus the linear equations is designed as ax+by+c=0 where x and y are variables and c is constant. This the generalized equations regarding mathematics which can further become more complex with the passage of time. Therefore this generalize equation will later be used in solving the equations related to complex lines, lines intersecting in between and many more.
Therefore let's presume two equations 3x+4y+6=0 and 3x+2y+6=0. Now to solve this equation we will have to apply a mathematical trick, we will first multiply the first equation with 1 and which will yield again 3x=4y=6=0 and the second equation by 2 and we will get 6x+4y+12=0. Now after eliminating both the equation we will get 3x+6=0 and x=-1/2.
And now we will put the value of x into the first equation and then we can find the value of y be -15/2 respectively. The entire process can be very exciting if we put the respective values of x and y on the equation we will get the right-hand side value which ultimately defines the value or the position of x and y in the plane sheet.
Math help is the best issue when comes to children. You can get the best software when comes to solving mathematical problems as there are much mathematical software. The beautiful part of the software is that it can help solve all the problems in the equations and thus can easily entice people. There are even endless numbers of software which can easily help children learn mathematics. The software includes learning abacus and playing with the calculation and thus finally figuring out the exact value of the question. Thus the significance can’t be overlooked. Mathematics is the very fabric which helps in understanding the very fabric of life and how it’s been made.
Different types of mathematical equations you can find in which linear, as well as quadratic equations, are common. These are the part of algebraic equations. The algebra is the part or branch of mathematics, and you can find its importance in mathematics. The algebraic system of equation contains different equations. Before learning about the system of equations, you must know some basics as-
Algebraic equations: The algebraic equation is the major part of mathematics in which various unknown values, mathematical signs, and constant values used to represent any number. While solving the algebraic expressions, you can get the values of unknown. More than one solution is possible for same variable value according to the equation.
Linear equation: liner equation includes one or more than one variable, but the variable does not include any higher degree. It means the variable has a first-order degree and you can find only one value for unknown.
Ex: x + 6 = 12
In result, you will get the value of x = 6
Quadratic equation: It comes under the algebraic equation in which you can find the second order degree of a variable. In a quadratic equation, you get two results for same variable or unknown value. For example- x² + 5x + 6 = 0
In which you can find values of x = -2 and -3
Exponential equation: It is another type of algebraic equation. In the system of equation in mathematics, exponential equations place an important role. The exponential equation shows successive increasing and decreasing variables.
Along with them, you can find various algebraic equations. Solving this algebraic equation becomes difficult when you do not have adequate knowledge of equations. Then, you need to join an online tutor to get adequate knowledge of it. On the other hand, you can choose the online platform that automatically solves the algebraic equations. You can also find the software which works offline.
How does the offline platform work?
You can choose either the website or the software for algebraic equation then you can easily solve it. First, you need to download the software on your PC. You can also buy CD to install the software on your personal computer. Now, you can use your PC to solve an algebraic equation. Some important formulas are preloaded into the software. It is not an offline tutor but solves the problem due to a pre-loaded program.
The user just needs to fill the question then press on the next tab. Now, you can get step by step solution of the equation. You can either choose the direct formula method to apply different method. The major benefit of choosing the software is that you can get the answer in few seconds. You can help your kid to solve their homework. The step by step solution of particular equation helps to understand the system of equations. Now, you can understand each operation, note down each step and understand what operations were used in the solution.
The system of equations is not difficult with the right mathematical software. It is your choices either use the particular website or download the software to solve an algebraic solution.
Mathematical has been one of the interesting subjects for many students since school years. Some of the students are afraid of its complexity and the numerical values. Simple mathematical rules such as addition, subtraction, multiplication, and division are really simple. But adding some unknown values into these expressions cause complexity in a mathematics calculation. These unknown values are basically expressed as X or Y. also other letters can be taken as the unknown. These unknown values are variables whose value varies with some numerical values. The entire expression is known as an algebra equation.
Algebra equation contains three terms namely variables, coefficients, and the constant value. Different type of algebraic equation and its form is available. You can analyze its type as-
Some digital platforms are available where the mathematical expert helps you in solving the exponential problems. Exponential expressions are one of the intimidating mathematical problems. To solve the algebra equation without graph calculator, you need to learn from basic. There is some basic function of algebra are-
Factors, base and exponential
In simple mathematical expression where you are instructed to multiply numbers and find out the single result. These numbers are known as factors. To understand better, consider an example as
3 x 5 = 15
Here 3 and 5 are the factors of 15 and the 15 is the product of 3 and 5. If you are going to find the factor of 49, then there are two factors i.e. 7 and 7. Consider one more example as to find a factor of 63. Here 7 and 9 are the factors and 3 and 3 are the factor of 9. So, you have 7, 3 and 3 factors of 63. The mathematical expression can be written as
3 x 5 = 15
7 x7 = 49
7 x 3 x 3 = 63
The last expression can be written as 7×3² = 63
The product of 3 x 3 can be written as 3² , and it is pronounced as three squared. Here the superscript is known as an exponent, and a lower number is called base. Now we know about base, factors, and exponent.
To add any number in which each has exponent value you have to find out the power of numerical term then multiply the number. Now you can easily add it. Similarly, if the math problem includes addition, multiplication, subtraction, and division then need to know the variable power then solve it.
3² + 4⁴ = 9 + 64 = 73
6x²+3x² = 9x²
This is the common rule to solve the exponential mathematical equation. The exponential calculator works similar but provides an instant result.
A Linear equation is a part of algebra in mathematics. In a linear equation, each term is a constant or it can be a product of constant of the variable. A very simple equation that can be written with one variable (x) could be ax + b=0, where a and b are constant and a ≠ 0. The constants a and b could be any numbers or parameters. Linear equations are universal in the applications of mathematics. Those equations that involve single variable will appear in simplest problems wherein one unknown parameter or quantity has to be solved from the other information which is given. In solving simple equations, one needs to use only elementary operations of arithmetic such as addition, multiplication, subtraction, and division.
How to solve linear equations?
One can solve the linear equations with visualization which is the ability or the process, and the product of the creation, use of, interpretation, and reflection which is used upon the pictures, diagrams, and images in the minds, paper or technological tools. The purpose of the solving is to depict and communicate the information which is thought upon and developed using previously unknown ideas and of advancing understandings.
Linear Equations with More Variables:
Equations can have one more one variables, such as equation with three variables x, y, and z is written asax + by + cz = 0, wherein a, b, and c are the constants and are any number except zero.
Equations with the exponents that are greater than one are known as non – linear equations. For example, axy + b = 0, where a and b are constants and a is not equal to zero. The equation has two variables x and y and is said to be non – linear as the sum of the exponents of the two variables in the first term is two.
Forms of Two – Dimensional Linear Equations
There are different forms in which the linear equations can be written. These are:
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