91Ó°ÊÓ

Involve dual investments. You invest 7200 dollar in two accounts paying \(8 \%\) and \(10 \%\) annual interest. At the end of the year, the accounts earn the same interest. How much was invested at each rate?

Graph the solution set of each system of linear inequalities. $$\left\\{\begin{array}{l}x-y \leq 3 \\\2 x+y \leq 4\end{array}\right.$$

Write a system of equations modeling the given conditions. Then solve the system by the substitution method and find the two numbers. The difference between two numbers is 1. The sum of the larger number and twice the smaller number is 7. Find the numbers.

Graph the solution set of each system of linear inequalities. If the system has no solutions, state this and explain why. $$\left\\{\begin{array}{l}x+y \geq 1 \\\x-y \geq 1 \\\x \geq 4\end{array}\right.$$

Write a system of equations modeling the given conditions. Then solve the system by the substitution method and find the two numbers. The difference between two numbers is \(5 .\) The sum of the larger number and twice the smaller number is \(14 .\) Find the numbers.

Graph the solution set of each system of linear inequalities. If the system has no solutions, state this and explain why. $$\left\\{\begin{array}{l}y>-3 x+5 \\\y \geq-x+3 \\\y \geq \frac{1}{2} x \\\x \geq 0 \\\y \geq 0\end{array}\right.$$

Graph the solution set of each system of linear inequalities. If the system has no solutions, state this and explain why. $$\left\\{\begin{array}{l}y \geq 2 x+2 \\\y<2 x-3 \\\x \geq 2\end{array}\right.$$

Find the slope and the \(y\) -intercept for the graph of each equation in the given system. Use this information (and not the equations' graphs) to determine if the system has no solution, one solution, or an infinite number of solutions. $$\left\\{\begin{array}{l}2 x+y=0 \\ y=-2 x+1\end{array}\right.$$

What does the graph of a system of linear inequalities represent?

The reason that systems of linear inequalities are appropriate for modeling healthy weight is because guidelines give healthy weight ranges, rather than specific weights, for various heights. I graphed the solution set of \(y \geq x+2\) and \(x \geq 1\) without using test points.