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# Systems of Linear Equations

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A company has an income of \$100,000 before paying taxes and a bonus. The bonus (B) is to be 20% of the income after deducting income taxes (T) but before deducting the bonus.

So B = 0.20(100,000 - T ).

Because the bonus is a deductible expense, the amount of income tax (T) at a 40% rate is 40% of the income after
deducting the bonus.

So T = 0.40(100,000 - B).

a) Use a graph to estimate the values of T and B that satisfy both equations.
b) Solve the system algebraically to find the bonus and the amount of tax.

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#### Solution Preview

The solution file is attached.

A company has an income of \$100,000before paying taxes and a bonus. The bonus B is to be 20% of the income after deducting income taxes T but before deducting the bonus. So B = 0.20(100,000 - T ). Because the bonus is a deductible expense, the amount of income tax T at a 40% rate ...

#### Solution Summary

A Complete, Neat and Step-by-step Solution is provided in the attached file regarding systems of linear equations. It uses a graph to estimate the values of T and B, and helps solve a system algebraically.

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