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Chapter 5: Problem 89
What is a half-plane?
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Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. A system of two equations in two variables whose graphs are two circles must have at least two real ordered-pair solutions
Exercises 37-39 will help you prepare for the material covered in the first section of the next chapter. Consider the following array of numbers: $$\left[\begin{array}{rrr}1 & 2 & -1 \\ 4 & -3 & -15\end{array}\right]$$ Rewrite the array as follows: Multiply each number in the top row by \(-4\) and add this product to the corresponding number in the bottom row. Do not change the numbers in the top row.
The group should write four different word problems that can be solved using a system of linear equations in two variables. All of the problems should be on different topics. The group should turn in the four problems and their algebraic solutions.
In Exercises 106-109, determine whether each statement makes sense or does not make sense, and explain your reasoning. When graphing \(3 x-4 y<12,\) it's not necessary for me to graph the linear equation \(3 x-4 y-12\) because the inequality contains a \(<\) symbol, in which equality is not included.
Without graphing, in Exercises 73鈥�76, determine if each system has no solution or infinitely many solutions. $$\left\\{\begin{array}{l} (x-4)^{2}+(y+3)^{2} \leq 24 \\ (x-4)^{2}+(y+3)^{2} \geq 24 \end{array}\right.$$
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