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Chapter 7: Problem 25
In Exercises 25-36, solve each system by the addition method. Be sure to check all proposed solutions. \(\left\\{\begin{array}{l}x+y=1 \\ x-y=3\end{array}\right.\)
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Without graphing, in Exercises 64-67, determine if each system has no solution or infinitely many solutions. \(\left\\{\begin{array}{l}3 x+y<9 \\ 3 x+y>9\end{array}\right.\)
In Exercises 29-30, find the vertex for the parabola whose equation is given by writing the equation in the form \(y=a x^{2}+b x+c\). \(y=(x-3)^{2}+2\)
a. Rewrite each equation in exponential form. b. Use a table of coordinates and the exponential form from part (a) to graph each logarithmic function. Begin by selecting \(-2,-1,0,1\), and 2 for \(y\). \(y=\log _{5} x\)
In Exercises 39-40, write each sentence as an inequality in two variables. Then graph the inequality. The \(y\)-variable is at least 4 more than the product of \(-2\) and the \(x\)-variable.
a. Create a scatter plot for the data in each table. b. Use the shape of the scatter plot to determine if the data are best modeled by a linear function, an exponential function, a logarithmic function, or a quadratic function. $$ \begin{array}{|c|c|} \hline \boldsymbol{x} & \boldsymbol{y} \\ \hline 0 & -3 \\ \hline 1 & -2 \\ \hline 2 & 0 \\ \hline 3 & 4 \\ \hline 4 & 12 \\ \hline \end{array} $$
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