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# College Algebra

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Please show work on problems attached.

14. Solve each system by substitution.

24. Solve each system by elimination.

32. Solve each system. State whether inconsistent or has infinitely many solutions. If the system has infinitely many solutions, write the solution set with y arbitrary.

34. Solve each system. State whether inconsistent or has infinitely many solutions. If the system has infinitely many solutions, write the solution set with y arbitrary.

52. Solve each system.

66. Solve each system. State whether inconsistent or has infinitely many solutions. If the system has infinitely many solutions, write the solution set with z arbitrary.

72. Solve each system. (Let = t and )

98. Patrick Summers wins \$200,000 in the Louisiana state lottery. He invests part of the money in real estate with an annual return of 3% and another part in a money market account at 2.5% interest. He invests the rest, which amounts to \$80,000 less than the sum of the other two parts, in certificates of deposit that pay 1.5%. If the total annual interest on the money is \$4,900, how much was invested at each rate?

10. Give all solutions for each nonlinear system of equations, including those with non-real complex components.

18. Give all solutions for each nonlinear system of equations, including those with non-real complex components.

32. Give all solutions for each nonlinear system of equations, including those with non-real complex components.

48. Solve each problem using a system of equations in two variables.

Find two numbers whose sum is 10 and whose squares differ by 20.

64. In electronics, circuit gain is modeled by , where R is the value of a resistor, t is temperature, , is the value of R at temperature t, and B is a constant. The sensitivity of the circuit to temperature is modeled by , If B=3.7 and t is 90 K(Kelvin), find the values of R and , that will make G = A and S = .001

20. Give the focus, directix, and axis for each parabola.

36. Write an equation for each parabola with vertex at the origin.

Through (-2, ), opening left

38. Write an equation for each parabola with vertex at the origin.

Through (2,-4), symmetric with respect to the y-axis.