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Solve for f, t, g, h, j, k, l, m
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h=i
Consider the fourth equation. Swap sides so that all variable terms are on the left hand side.
i=g
Consider the third equation. Insert the known values of variables into the equation.
g=i
Swap sides so that all variable terms are on the left hand side.
i=f\times 5
Consider the second equation. Insert the known values of variables into the equation.
\frac{i}{5}=f
Divide both sides by 5.
\frac{1}{5}i=f
Divide i by 5 to get \frac{1}{5}i.
f=\frac{1}{5}i
Swap sides so that all variable terms are on the left hand side.
\frac{1}{5}it=\frac{3t+3}{5}
Consider the first equation. Insert the known values of variables into the equation.
it=3t+3
Multiply both sides of the equation by 5.
it-3t=3
Subtract 3t from both sides.
\left(-3+i\right)t=3
Combine it and -3t to get \left(-3+i\right)t.
t=\frac{3}{-3+i}
Divide both sides by -3+i.
t=\frac{3\left(-3-i\right)}{\left(-3+i\right)\left(-3-i\right)}
Multiply both numerator and denominator of \frac{3}{-3+i} by the complex conjugate of the denominator, -3-i.
t=\frac{-9-3i}{10}
Do the multiplications in \frac{3\left(-3-i\right)}{\left(-3+i\right)\left(-3-i\right)}.
t=-\frac{9}{10}-\frac{3}{10}i
Divide -9-3i by 10 to get -\frac{9}{10}-\frac{3}{10}i.
f=\frac{1}{5}i t=-\frac{9}{10}-\frac{3}{10}i g=i h=i j=i k=i l=i m=i
The system is now solved.