91Ó°ÊÓ

In \(2013,\) the top three donors of foreign aid were the United States, Great Britain, and Germany. The total amount of their aid was \(\$ 63.5\) billion. Together, Great Britain and Germany donated \(\$ 0.5\) billion more than the United States did. The United States donated \(\$ 17.4\) billion more than Germany did. (Source: Organization for Economic Cooperation and Development) How much in foreign aid did each country donate?

Solve using the substitution method. Use a graphing calculator to check your answer. $$\begin{aligned} 5 x+3 y &=-1 \\ x+y &=1 \end{aligned}$$

Solve using the substitution method. Use a graphing calculator to check your answer. $$\begin{aligned} &2 x-y=2\\\ &4 x+y=3 \end{aligned}$$

Solve using the elimination method. Also determine whether the system is consistent or inconsistent and whether the equations are dependent or independent. Use a graphing calculator to check your answer. $$\begin{aligned} &x+2 y=7\\\ &x-2 y=-5 \end{aligned}$$

Solve using the elimination method. Also determine whether the system is consistent or inconsistent and whether the equations are dependent or independent. Use a graphing calculator to check your answer. $$\begin{array}{c} x-3 y=2 \\ 6 x+5 y=-34 \end{array}$$

Solve the system of equations using the inverse of the coefficient matrix of the equivalent matrix equation. $$\begin{aligned} 2 w-3 x+4 y-5 z &=0 \\ 3 w-2 x+7 y-3 z &=2 \\ w+x-y+z &=1 \\\\-w-3 x-6 y+4 z &=6 \end{aligned}$$

\(0.3 x-0.2 y=-0.9\) \(0.2 x-0.3 y=-0.6\) (Hint: since each coefficient has one decimal place, first multiply each equation by 10 to clear the decimals.)

Use synthetic division to find the function values. $$f(x)=2 x^{4}-x^{3}+5 x^{2}+6 x-4 ; \text { find } f(3)$$

Determine whether the statement is true or false. If a system of two linear equations in two variables is dependent, then it has infinitely many solutions.

Determine whether the statement is true or false. It is possible for a system of two linear equations in two variables to be consistent and dependent.