Without graphing, answer the questions for the following linear system. \[ \begin{aligned} y-x=-5 \\ x+y=8\end{aligned} \] (a) Is the system inconsistent, or are the equations dependent, or neither? (b) Is the graph a pair of intersecting lines, a pair of parallel lines, or one line? (c) Does the system have one solution, no solution, or an infinite number of solutions?

Solve the following equations and inequalities analytically. Support your solutions graphically. \( \begin{array}{lll}\begin{array}{ll}\text { (a) }|2 x+1|+3=5 & \text { (b) }|2 x+1|+3 \leq 5 \\ \text { (c) }|2 x+1|+3 \geq 5\end{array} \\ \text { A. The solution set is the finite set of real numbers }\{ \\ \text { (a) Find the solution for }|2 x+1|+3=5 \text {. Select the correct choice below, and fill in the } \\ \text { answer box if necessary. } \\ \text { expression. Use a comma to separate answers as needed.) } \\ \text { B. The solution set is the interval } \square \text {. } \\ \text { (Type your answer in interval notation. Use integers or fractions for any } \\ \text { numbers in the expression.) } \\ \text { C. The solution set is } \varnothing \text {. }\end{array} \).

(a) Find the solution for \( |2 x+1|+3=5 \). Select the correct choice below, and fill in the answer box if necessary. A. The solution set is the finite set of real numbers \( \{ \). (Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. The solution set is the interval (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

Solve the following system of equations by the addition method. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent. \[ \begin{aligned} 4 x+3 y & =-14 \\ 2 x-y & =-12\end{aligned} \]

5) Sea una función lineal cuya gráfica pasa por los puntos \( (6,3) \) y \( (-2,-1) \). a) Determine la función b) ¿Cuál es el valor de \( f(-3) \) y de \( f(8) \) ? c) ¿Es creciente o decreciente?

b. Two consecufive number are sucl that the sum of thrice the smaller and twice the larger is 17. Find, correct to three significant figures the smaller number as a percen - tage of the sum of the. two numbers.