As a result of several mergers and acquisitions, stock in four companies has been

distributed among the companies. Each row of the following table gives the

percentage of stock in the four companies that a particular company owns and the

annual net income of each company.

So company A holds $70\%$ of its own stock, $2\%$ of the stock in company B$,11\%$ of the

stock in company $C,$ etc. For the purpose of assessing a state tax on

corporate income, the taxable income of each company is defined to be its share of

its own annual net income plus its share of the taxable income of each of the

other companies, as determined by the percentages in the table. What is the taxable

income of each company $($to the nearest thousand dollars$)?$

Use the variables $x_1$ to represent taxable income of company $A,x_2$ to

represent taxable income of company $B,x_3$ to represent taxable income of

company $C,$ and $x_4$ to represent taxable income of company $D,$ and write the

system of equations that can be used to find all of the taxable incomes in

millions of dollars.

The equation that represents the calculation of company A$\text{'}$s taxable income is

$x_1-0\mathrm{.}02x_2-0\mathrm{.}11x_3-0\mathrm{.}12x_4=2\mathrm{.}59.$

The equation that represents the calculation of company B$\text{'}$s taxable income is

$-0\mathrm{.}13x_1+x_2-0\mathrm{.}14x_3-0\mathrm{.}12x_4=3\mathrm{.}237.$

The equation that represents the calculation of company C$\text{'}$s taxable income

is $-0\mathrm{.}07x_1-0\mathrm{.}13x_2+x_3-0\mathrm{.}14x_4=2\mathrm{.}077.$

The equation that represents the calculation of company D$\text{'}$s taxable income

is $-0\mathrm{.}1x_1-0\mathrm{.}02x_2-0\mathrm{.}08x_3+x_4=2\mathrm{.}666.$

$($Simplify your answers. Use integers or decimals for any numbers in

the equations.$)$

The taxable income for company $A$ is $ million. The taxable income for

company $B$ is $ million. The taxable income for company $C$ is $ million.

The taxable income for company $D$ is $ million.

$($Round to the nearest thousandth as needed.$)$