91Ó°ÊÓ

Classify the following statements as either true or false. The elimination method works especially well when the coefficients of one variable are opposites of each other.

Classify each of the following statements as either true or false. When solving a system of equations algebraically leads to a false equation, the system has no solution.

Classify each of the following statements as either true or false. When solving a system of two equations algebraically leads to an equation that is always true, the system has an infinite number of solutions.

Solve using the elimination method. If a system has an infinite number of solutions, use set-builder notation to write the solution set. If a system has no solution, state this. \(x-y=6\) \(x+y=12\)

Determine whether the ordered pair is a solution of the given system of equations. Remember to use alphabetical order of variables. $$ \begin{aligned} (4,-2) ; &-3 x-2 y=-8 \\ 8 &=3 x+2 y \end{aligned} $$

Asel's two student loans totaled \(\$ 12,000\). One of her loans was at \(6.5 \%\) simple interest and the other at \(7.2 \%\). After one year, Asel owed \(\$ 811.50\) in interest. What was the amount of each loan?

Two cars leave Salt Lake City, traveling in opposite directions. One car travels at a speed of \(80 \mathrm{km} / \mathrm{h}\) and the other at \(96 \mathrm{km} / \mathrm{h}\). In how many hours will they be \(528 \mathrm{km}\) apart?

Solve using the elimination method. If a system has an infinite number of solutions, use set-builder notation to write the solution set. If a system has no solution, state this. \(\begin{aligned} x+\frac{9}{2} y &=\frac{15}{4} \\ \frac{9}{10} x-y &=\frac{9}{20} \end{aligned}\)

Solve using a system of equations. The sum of two numbers is \(83 .\) One number is 5 more than the other. Find the numbers.

Two angles are supplementary. One angle is \(15^{\circ}\) more than twice the other. Find the measure of each angle.