Assignment:
Q1. Solve each system by substitution.
4x + 5y = 7
9y = 31 + 2x
Q2. Solve each system by elimination.
12x - 5y = 9
3x - 8y = -8
Q3. 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.
3x + 2y = 5
6x + 4y = 8
Q4. 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.
3x + 5y = -2
9x + 15y = -6
Q5. Solve each system.
4x - 3y + z = 9
3x + 2y - 2z = 4
x - y + 3z = 5
Q6. 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.
3x + y + 3x = 1
x + 2y - z = 2
2x - y + 4z = 4
Q7. Solve each system. (Let 1 / x = t and 1 / y )
2/x + 3/y = 18
4/x - 5/y = -8
Q8. 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?
Q9. Give all solutions for each nonlinear system of equations, including those with non-real complex components.
x2 + y = 2
x - y = 0
Q10. Give all solutions for each nonlinear system of equations, including those with non-real complex components.
x2 + y2 = 10
2x2 + y2 = 17
Q11. Give all solutions for each nonlinear system of equations, including those with non-real complex components.
-5xy + 2 = 0
x - 15y = 5
Q12. Solve each problem using a system of equations in two variables.
Find two numbers whose sum is 10 and whose squares differ by 20.
Q13. In electronics, circuit gain is modeled by G = Bt / R + R1 , where R is the value of a resistor, t is temperature, R1 , is the value of R at temperature t, and B is a constant. The sensitivity of the circuit to temperature is modeled by S = BR / (R + R1)2 , If B=3.7 and t is 90 K(Kelvin), find the values of R and , that will make G = A and S = .001
Q14. Give the focus, directix, and axis for each parabola.
x2 = 1/8 y
Q15. Write an equation for each parabola with vertex at the origin.
Through (-2,-2√2 ), opening left
Q16. Write an equation for each parabola with vertex at the origin.
Through (2,-4), symmetric with respect to the y-axis.
Provide complete and step by step solution for the question and show calculations and use formulas.