Equations
An equations is a combination of one or more terms separated with equal symbol "=". Terms can be numerical, alphanumerical, expression etc.
Different type of equations.
1.) Equations which have solution: In these types of equation we can find the value of variable like a, b, c.
Examples:
a.) 5x + y = 12 , 7x - 2y = 21
b.) 2a - 3b = 6 , 5a + b = 10
After solving these two equation we will get the value of x and y.
2.) Equation without solution: An equation which have no solution. Means we cannot find the value of variable.
0 = -2, 0 = 12 ,7=8
Examples: a.) 5a + 4 -7a = 6a +7 - 8a - 5
Step:1. 4 + 5a - 7a = 6a – 8a + 7 - 5
Step:2. 4 - 2a = -2a + 2
Step:3. 2a – 2a = 2 - 4
Step: 4. 0 = -2
Example b.) 7x - 6 = 7x + 6.
Step:1. 7x - 7x = 6 + 6
Step:2. 0 = 12 etc.
For equations with solution, we can solve the equation by the following method.
1)Elimination method
2)Substitution method
3) Graphing method.
4.) Trial and error method.
5.) Taylor method.
6.) Numerical Method
7.) Solving Equations usingInverse Functions
Types of Equation: An equation play a very important role in the mathematics. We are solving many problems with the help of equation. There are manytypes of equations.
1.) Linear equation : A linear equation is very similar to analgebraic equation of the from
y = mx + b.
Where m is slope , And b is y-intercept.
Example : a) y = 8x - 9
b) y = - x - 13.
2.) Radical equation: Radical equation is an equation which has the fractional exponent over variables.
Fractional exponent is the another way to representthe radicals or roots
Example : a) $\sqrt{x}$ + 15 = 32.
b) $\sqrt{x^2 - 5}$ + x - 7 = 4
3.) Constant equation: The equation which variable value cannot be change is known as Constant equation.
Examples : a) x - 4 = 0
b) 6p+ 8 = 7.
4.) Quadratic equation: An equation which has one or more terms but the highest degree is two is known asquadratic equation,
The standard from of this equation is ax2 + bx + c =0.
Examples: a) 4x2 + 6x - 5 = 0.
b) 4y2 + 44y + 8 =0.
c) 5a2 - 5a = 12
5.) Equation with different type of variables:
a) Equation with one type of variables: The equation which has only one variable is known as equation with one type of variables.
Examples: i ) 11x + 7 = 17
ii ) 5a - 8 = 0
iii ) 9a = 63.
b) Equation with two types of variables: The equation which has only two types of variable is know as equation with two types of variables.
Examples: i ) 7x + 7y = 12
ii ) 8a - 8d = 74
iii ) 9a + 6b - 82 = 0.
c) Equation with three types of variables: The equation which have only three types of variable is known as equation with three types of variables.
Examples: i ) 5x + 5y - 2z = 72
ii ) 11a - 6b + 3c = 34
iii ) 6p + 18q -7r + 2 = 0.
6.) Exponential Equation: An exponential equation is very much similar to a number haves exponents.
Exponent : It will be easy to understand with an examples
Examples : i ) ab Here "a" is base and "b" is exponent.
Here, "a" multiplies "b" times.
ii ) 42 Here 4 is base and 2 is exponent.
Here, 4 multiply 2 times.
(4)(4) = 16.
Definition of exponential equation: The definition of exponential equation is which follows this "ex = 0".
Examples: i ) 8x = 32.
ii ) P3 = 64.
iii ) 10a = 104
iv ) xy-1 = x6
7.) Differential Equations:
Following are the types of Differential equation.
a.) Ordinary Differential Equations: It is depend on only oneindependent variable.
Example: $\frac{dy}{dx}$ = my(x) , because y depends only on x.
b.) Order of a Differential Equation: lt is defined as the highest degree of derivative entering the equation.
Example : $\frac{dy}{dx}$ = -mx This is second-order differential equation because it involvessecond derivatives.
A number which satisfies the given equation is called a solution or root of that. ‘Satisfying the equation’ means that if the variable (literal) involved in this is replaced by the number, then both sides of that become equal. The process of finding the particular value of the variable (literal) which makes both sides of the equation equal is called solving the equation. Below are rules that need to be followed in solving equations.
Rule 1:- If equals are added to equals, the sums are equals. In other words, you can add the same number to both sides of an equation.
Rule 2:- If equals are subtracted from equals, the remainders are equal. In other words, you can subtract the same number from both sides of an equation.
Rule 3:- The two sides of an equation may be multiplied by same non-zero number For example, if $\frac{x}{5}$ = 7, then $\frac{x}{5}$ × 5 = 7 × 5.
Rule 4:- The two sides of an equation may be divided by same non-zero number
Equation is one of the most important calculations in algebra and the most essential concept of math. It deals mainly with algebraic expressions.
There are different types of equations: radical, parabola, hyperbola, linear, differential, partial differential and quadratic equations. Learn about all these concepts with our tutor, understand the depth of the topics and get a hold over the whole concept of equations. Below stated are the different types of algebra equations frequently asked by students and how our tutors help you make them easier.
Linear equations:
Linear equation is any equation that when graphed produces a straight line. There are various types of equations; none except linear equations will produce a straight line when graphed. Get help in solving linear equations and find easy steps to follow. Students can learn about graphing of various equations like the graph of linear equations also.
Differential equations:
An equation involving one dependent variable and its derivatives with respect to one or more independent variables is called Differential Equations. Get help in solving equations, solve equations with easy steps and be an expert.
Partial differential equations
A partial differential equation is an equation which contains one or more partial derivatives. The order of the partial differential equation is that of the derivative of highest order in the equations. Connect to a tutor and work out equations with proper understanding.
Quadratic equations
The equations that are having the highest degree term x2 or second degree are called as Quadratic Equations. Learn how to solve quadratic equations with an online tutor, and make the topic easy and interesting.
Radical equations
Radical are also called as roots of an expression. Get help in solving radical expressions and solve with easy steps and methods.
Parabola equation
A parabola is set of all points in the plane which are equidistant from a fixed line and a fixed point not on the line. Solve a parabola with graphs and easy steps.
Hyperbola equation
A hyperbola is the set of all points in the plane, the difference of whose distances from two fixed distinct points is a given positive constant that is less than the distance between the fixed points.
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