Solutions to Try Its

1. $\left(-\frac{1}{2},\frac{1}{2}\right)$ and $\left(2,8\right)$

2. $\left(-1,3\right)$

3. $\left\{\left(1,3\right),\left(1,-3\right),\left(-1,3\right),\left(-1,-3\right)\right\}$

4. Shade the area bounded by the two curves, above the quadratic and below the line.

Solutions to Odd-Numbered Exercises

1. A nonlinear system could be representative of two circles that overlap and intersect in two locations, hence two solutions. A nonlinear system could be representative of a parabola and a circle, where the vertex of the parabola meets the circle and the branches also intersect the circle, hence three solutions.

3. No. There does not need to be a feasible region. Consider a system that is bounded by two parallel lines. One inequality represents the region above the upper line; the other represents the region below the lower line. In this case, no points in the plane are located in both regions; hence there is no feasible region.

5. Choose any number between each solution and plug into $C\left(x\right)$ and $R\left(x\right)$. If [latex]C\left(x\right)

41.

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49. $\left(-2\sqrt{\frac{70}{383}},-2\sqrt{\frac{35}{29}}\right),\left(-2\sqrt{\frac{70}{383}},2\sqrt{\frac{35}{29}}\right),\left(2\sqrt{\frac{70}{383}},-2\sqrt{\frac{35}{29}}\right),\left(2\sqrt{\frac{70}{383}},2\sqrt{\frac{35}{29}}\right)$

51. No Solution Exists

53. $x=0,y>0$ and [latex]0