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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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