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

    3(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?

    3x + 5   =   11     . . .  our given equation
       - 5      - 5     . . .  subtract 5 from each side to get constants on the right

3x = 6 . . . the result

3x / 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 "QuadraticEquation?s".

CategoryMath

See also: QuadraticFormula, EigenValue, EigenVector, MatrixAnalysis


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