Solving Linear Equations
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An equation has to have an equals sign, as in 3x + 5 = 11 .
A solution to an equation is a number that can be plugged in for the variable to make a true number statement.
For example, putting 2 in for x above in 3x + 5 = 11 gives
- (2) + 5 = 11 , which says 6 + 5 = 11 ; that's true! So 2 is a solution.
But how to start with the equation, and get (not guess) the solution?
- x + 5 = 11 . . . our given equation
- 5 - 5 . . . subtract 5 from each side to get constants on the right
- x = 6 . . . the result
- x / 3 = 6 / 3 . . . divide both sides by 3 to isolate the x
x = 2 . . . the solution (same as before!)
. . . . . . . . . . . . . We have solved the equation.
. . . . . . . . . . . . . And we have done the CheckBySubstitution (UnitTest).
The thing that makes this equation linear is that the highest power of x is x^1 (no x^2 or other powers; those are "QuadraticEquations".
See also: QuadraticFormula, EigenValue, EigenVector, MatrixAnalysis
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