91Ó°ÊÓ

In Exercises \(43-46,\) let \(x\) represent one number and let \(y\) represent the other number. Use the given conditions to write a system of equations. Solve the system and find the numbers. Three times a first number decreased by a second number is 1. The first number increased by twice the second number is \(12 .\) Find the numbers.

Which one of the following is true? a. A system of two equations in two variables whose graphs represent a circle and a line can have four real solutions. b. A system of two equations in two variables whose graphs represent a parabola and a circle can have four real solutions. c. A system of two equations in two variables whose graphs represent two circles must have at least two real solutions. d. A system of two equations in two variables whose graphs represent a parabola and a circle cannot have only one real solution.

Graphing utilities can be used to shade regions in the rectangular coordinate system, thereby graphing an inequality in two variables. Read the section of the user's manual for your graphing utility that describes how to shade a region. Then use your graphing utility to graph the inequalities. $$ y \geq x^{2}-4 $$