Differential Equations - Systems of Equations (Elimination Method)

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Solve the system of differential equations:
x''(t) + y'(t) - x(t) + y(t) = -1
x'(t) + y'(t) - x(t) = t^2
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Ahh I see now. So the shortcut of removing derivatives of y (leaving y and x terms behind) will only work in specific questions (like the one in this video). If it's not possible to remove derivatives of y in any question, then we will have to eliminate x and find y ( and do the whole lengthy process of finding y(t), just like we found x(t).

tbg
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6:18 How did you get ((r^2)-1)*(r-1)? This doesnt make sense to me

reeceengineering
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How is t square is equal to negative one

puremaths