Solving Two Simultaneous Linear Equations
To be solved, word or story problems must be translated into equations with algebraic expressions that contain constants and variables. Simple word problems may not need variables at all. Some are more conveniently soved with the introduction of one or more variables. Usually, the number of resulting equations equals the number of the introduced variables. The simplest of the multivariable/equation problems is that with two variables and two linear equations. As always, there are many ways to approach the same problem. Below we look into two such ways of solving a linear system of two simultaneous equations.
The first approach is based on the fact that, if two equations are satisfied, so is their difference (or the sum, for that matter.) Also, this is one of Euclid's common notions that if two equal quantities are multiplied by the same factor, the results remain equal. Using that, we cam multiply the two equations by such factors as to make the coefficients by the same variable equal. Subtracting then one equation from the other eliminates that variable.
(Note: In the applet below, all underlied words and numbers can be clicked on. Click, click, click ... and see what happens.)
Another approach is to express one of the unknowns in terms of the other from one of the equations and substitute that into the other equation. The result is one equation with one unknown. We solve this first and then find the first unknown. See for yourself:
(There are many more word problems discussed and solved at this site. The math tutorial continues with a similar approach over several additional examples.)
- Problems of class a + x = b
- Problems of class a · x = b
- From Word Problem to Equation
- Problems of class x / a = b / c
- Problems of class x = a + b
- Problems of class x = a + b (II)
- Problems of class x = a × b
- Solving Two Simultaneous Linear Equations
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