CHAPTER 14 REVIEW EXERCISES

CONCEPT CHECK EXERCISES

Determine each of the following as being either true or false. If it is false, explain why.

To get the calculator display of the equation $2 x^{2} + y^{2} = 4,$ let $y_{1} = \sqrt{4 - 2 x^{2}} .$
A solution of the system $x^{2} + 2 y^{2} = 9, 2 x^{2} - y = 3,$ is $(- 1, 2) .$
A solution of the equation $8 x^{- 4} - 2 x^{- 2} - 1 = 0$ is $(\sqrt{2}, 1) .$
A solution of the equation $\sqrt{3 - x} + 1 = 0$ is $x = 2.$

In Exercises 5–14, solve the given systems of equations by use of a calculator.

$\begin{array}{l} x + 2 y = 9 \\ y = 3 x^{2} \end{array}$
$\begin{array}{l} x + y = 3 \\ x^{2} + y^{2} = 25 \end{array}$
$\begin{array}{rcl} \frac{1}{2} x + \frac{1}{3} y & = & 1 \\ x^{2} + 4 y^{2} & = & 4 \end{array}$
$\begin{array}{l} x^{2} - 2 y = 0 \\ y = 3 x - 5 \end{array}$
$\begin{array}{l} y = x^{2} + 1 \\ 4 x^{2} + 16 y^{2} = 35 \end{array}$
$\begin{array}{rcl} \frac{x^{2}}{4} + y^{2} & = & 1 \\ x^{2} - y^{2} & = & 1 \end{array}$
$\begin{array}{rcl} y & = & 11 - x^{2} \\ y & = & 2 x^{2} - 1 \end{array}$
$\begin{array}{l} x^{2} y = 63 \\ y = 25 - 2 x^{2} \end{array}$
$\begin{array}{rcl} y & = & x^{2} - 2 x \\ y & = & 1 - e^{- x} + x \end{array}$
$\begin{array}{rcl} y & = & 2 \ln x \\ y & = ... \end{array}$

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