Use a system of equations to solve the following problems. See the earlier examples.

What choice of a, b, and c will force the graph of the polynomial $f(x)=a x^2+b x+c$ to have a $y$-intercept of 5 and to pass through the points $(1,3)$ and $(2,0)$?

Describe how a mountain system affects the distribution of precipitation on its windward side as compared to its leeward side.

Solve the given problems. Find a system of inequalities that would describe the region within the triangle with vertices $(0,0)(0,4),$ and $(2,0)$ .

Solve the given problems using inequalities. (All data are accurate to at least two significant digits.)

Find a system of inequalities that would describe the region within the quadrilateral with vertices $(0,0),(4,4),(0,-3),$ and $(4,-3)$ .

In this exercise, make the given changes in the indicated examples of this section and then solve the resulting problems.

In the said example $3$, change the $+$ to $-$ in the second equation and then solve the system of equations.

In the following exercise, find $X_2$ (the probability distribution of the system after two observations) for the distribution vector $X_0$ and the transition matrix $T$.

$$X_0=\left[\begin{array}{l}.6 \\ .4\end{array}\right], T=\left[\begin{array}{ll}.4 & .8 \\ .6 & .2\end{array}\right]$$

Solve the given problems using inequalities. (All data are accurate to at least two significant digits.)

Describe the region that satisfies the system $y \geq 2 x-3, y<2 x-3$

Solve the given problems. Use a calculator to solve if necessary.
Solve the following system algebraically: $y=x^{4}-11 x^{2} ; \quad y=12 x-4$

Name three problems that may result if a hydraulic system is consistently operated at lower than recommended temperatures.

Using complete sentence, answer the following question.
Name and briefly describe three problems of the lymphatic system

Solve the given problems. Where appropriate, set up the required equations.

Solve the following system algebraically: $x^{2}=y+3 ; x y=2$

In the following exercise, find $X_2$ (the probability distribution of the system after two observations) for the distribution vector $X_0$ and the transition matrix $T$.

$$X_0=\left[\begin{array}{l}.35 \\ .25 \\ .40\end{array}\right], T=\left[\begin{array}{lll}.2 & .1 & .3 \\ .5 & .4 & .4 \\ .3 & .5 & .3\end{array}\right]$$

Solve the given problems.
Use a graphing calculator to solve the following system of three equations: $x^2+y^2=13, y=x-1, x y=6$.

Solve the given problems.

Draw a sketch of the graph of the region in which the points satisfy the system of inequalities $xy<4$, $y>x$.