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linear equations

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r(n) means "r subscript n"

The function y=e^(rx) has two values, r(1) and r(2) that satisfy the equation
2y''+y'-y=0.

How can I show that every number of the family of functions

y=a*e^[r(1)x] + b*e^[r(2)x]

is also a solution to the equation 2y''+y'-y=0?

https://brainmass.com/math/linear-algebra/every-number-family-functions-416011

Solution Summary

This solution exemplifies linear equations.

\$2.19

Solving Systems of linear equations

Systems of linear equations

Books and magazines. At Gwen's garage sale, all books were one price, and all magazines were another price.
Harriet bought four books and three magazines for \$1.45,and June bought two books and five magazines for \$1.25.
What was the price of a book and what was the price of a magazine?

Solving by Substitution

Solve each system by substitution. Determine whether the equations are independent, dependent, or inconsistent.

y=-3x+19
y=2x-1

y=-4x-7
y=3x

y=x+4
3y-5x=6

x-2y=-1
-x+5y=4

3x-5y=-11
x-2y=11

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