Solve for α, β, x
x=3
\alpha =2
\beta =-1
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x=2\alpha +\beta 1=\alpha +\beta 5=3\alpha +\beta
Reorder the equations.
\beta =1-\alpha \alpha =\frac{5}{3}-\frac{1}{3}\beta
Solve the second equation for \beta and the third equation for \alpha .
\alpha =\frac{5}{3}-\frac{1}{3}\left(1-\alpha \right)
Substitute 1-\alpha for \beta in the equation \alpha =\frac{5}{3}-\frac{1}{3}\beta .
\alpha =2
Solve \alpha =\frac{5}{3}-\frac{1}{3}\left(1-\alpha \right) for \alpha .
\beta =1-2
Substitute 2 for \alpha in the equation \beta =1-\alpha .
\beta =-1
Calculate \beta from \beta =1-2.
x=2\times 2-1
Substitute -1 for \beta and 2 for \alpha in the equation x=2\alpha +\beta .
x=3
Calculate x from x=2\times 2-1.
\alpha =2 \beta =-1 x=3
The system is now solved.
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