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## Homework Statement

Systems of first order equations can sometimes be transformed into a single equation of

higher order. Consider the system

(1) x

_{1}' = -2x

_{1}+ x

_{2}

(2) x

_{2}' = x

_{1}- 2x

_{2}

Solve the first equation for x

_{2}and substitute into the second equation, thereby obtaining a second order equation for x

_{1}. Solve this equation for x

_{1}and then determine x

_{2}also.

## Homework Equations

## The Attempt at a Solution

Solving (1) for x

_{2}yields:

x

_{2}= x

_{1}' + 2x

_{1}

Substituting into (2) yields:

x

_{2}' = x

_{1}- 2(x

_{1}' + 2x

_{1})

Simplifying...

x

_{2}' = -3x

_{1}- 2x

_{1}'

How am I supposed to solve this now with the x

_{2}' term there?