# Solution of Equation - Methods For Solving Simple Equations, Solving More Complex Equations, Solving Multivariable Equations, Solving Second Degree And Higher Equations

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The solution of an equation is the set of all values which, when substituted for unknowns, make an equation true. For equations having one unknown, raised to a single power, two fundamental rules of **algebra**, including the additive property and the multiplicative property, are used to determine its solutions. Solutions for equations with multiple unknown variables are found by using the principles for a system of equations. Equations with terms raised to a power greater than one can be solved by factoring and, in some specific cases, by the quadratic equation.

The idea of a solution of equations has existed since the time of the Egyptians and Babylonians. During these times, they used simple algebraic methods to determine solutions for practical problems related to their everyday life. The methods used by the ancients were preserved in a treatise written by the Arabian mathematician Al-Kowarizmi (A.D. 825). In this work, he includes methods for solving linear equations as well as second degree equations. Solutions for some higher degree equations were worked out during the sixteenth century by an Italian mathematician named Gerolamo Cardano (1501-1576).

## Additional Topics

Using the two fundamental rules of algebra, solutions to many simple equations can be obtained. The first rule states that the same quantity can be added to both sides of an equation without changing the solution to the equation. For example, the equation x + 4 = 7 has a solution of x = 3. According to the first rule, we can add any number to both sides of the equation and still get the same solut…

Most equations are given in a more complicated form which can be simplified. Consider the equation 4x - x - 5 = 2x + 7. The first step in solving this equation is to combine like terms on each side of the equation. On the right side there are no like terms, but the 4x and -x on the left side are like terms. This equation, when simplified, becomes 3x - 5 = 2x + 7. The next step is to eliminate the …

Many algebraic equations contain more than one variable, so the complete solution set can not be found using the methods described thus far. Equations with two unknowns are called linear equations and can be represented by the general formula ax + by = c; where a, b, and c are constants and x and y are variables. The solution of this type of equation would be the ordered pair of x and y which make…

To use the quadratic formula, numbers for a, b, and c are substituted into the equation, and the solutions for x are determined. …

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## User Comments

about 8 years ago

help soving this problem. Solutions of equations. from the developing skills in algebra Book A (1984 by Dale Seymour publications.

4(2x + 7)=108

about 10 years ago

i indeed thank the maker of this page

you are really helpful

about 8 years ago

denis

щчень нужно

over 7 years ago

gemz

can u pls help me solving this problem?

7.342miles/hour=_____km/seconds

convert miles/hour to km/sec

pls help me tnx

about 10 years ago

This web page really helped my daughter out with understanding equations. I thank the maker of this page.

Thank You

-Tina

over 7 years ago

khate

haha .. nahihirapan ako ! sagad.

over 7 years ago

1.13x+.70y=500

x+y=500