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Chapter 5: Problem 88
Explain how to solve a system of equations using the addition method. Use \(3 x+5 y=-2\) and \(2 x+3 y=0\) to illustrate your explanation.
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Explain how to solve a nonlinear system using the addition method. Use \(x^{2}-y^{2}-5\) and \(3 x^{2}-2 y^{2}-19\) to illustrate your explanation.
Exercises 116-118 will help you prepare for the material covered in the next section. a. Graph the solution set of the system: $$\left\\{\begin{aligned} x & \geq 0 \\ y & \geq 0 \\ 3 x-2 x & \leq 6 \\ y & \leq-x+7 .\end{aligned}\right.$$ b. List the points that form the corners of the graphed region in part (a). c. Evaluate \(2 x+5 y\) at each of the points obtained in part (b).
Determine whether each statement makes sense or does not make sense, and explain your reasoning. Because \(x+5\) is linear and \(x^{2}-3 x+2\) is quadratic, I set up the following partial fraction decomposition: $$\frac{7 x^{2}+9 x+3}{(x+5)\left(x^{2}-3 x+2\right)}=\frac{A}{x+5}+\frac{B x+C}{x^{2}-3 x+2}$$
When is it easier to use the addition method rather than the substitution method to solve a system of equations?
Explain how to solve a nonlinear system using the substitution method. Use \(x^{2}+y^{2}-9\) and \(2 x-y-3\) to illustrate your explanation.
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