Algebra is one of the chief branches of mathematics. Mastery of mathematics depends on a sound understanding of algebra. Engineers and scientists use algebra every day. Business and industry rely on algebra to help solve many problems. Because of its importance in modern living, algebra is studied in schools and colleges in all parts of the world.
Unknown numbers in algebra are represented by letters, such as x or y. In some problems, the letter can be replaced by only one number. A simple example would be x + 3 = 8. For this statement to be true, x must be 5, because 5 + 3 = 8. In other problems, the letter may be replaced by one of many numbers. For example, for the algebraic statement x + y = 12 to be true, x would be 6 if y is 6, or x would be 4 if y is 8. In such an algebraic statement, you can find many values for x that make true statements if you give different values to y.
People can use algebra to solve problems in ways that are beyond the range of arithmetic alone. For example:
An airplane travels 1,710 kilometers in 4 hours flying with the wind, but it travels only 1,370 kilometers in 5 hours flying against the wind. The speed of the airplane in relation to the air is the same in both directions, and the wind speed is constant. What is (1) the speed of the airplane in relation to the air and (2) the speed of the wind?
The key to solving this problem is to use letters to represent the two unknown numbers. For example, you might use x to represent the speed of the plane relative to the air, and y to represent wind speed. Using letters in this way is not part of arithmetic, but is an essential part of algebra.
