1. Pen Tool McGraw-Hill Ryerson Pre-Calculus 11 Chapter 8 Systems of Equations Section 8.2 Click here to begin the lesson

2. Pen Tool Solving Systems Algebraically Chapter 8 Use the method of substitution to solve the system of equations. Rearrange the second equation for y. Substitute the value of y into the first equation. Simplify and solve the resulting quadratic equation. Using the values of x, determine the value of y. Verify the solutions. Click here for the solution. 1 2

3. Pen Tool Chapter 8 Solving Systems Algebraically Use the method of elimination to solve the given system of equations. Subtract the equations to eliminate the variable y. Solve the resulting quadratic equation. Using the values of x, determine the value of y. 1 2 Click here for the solution.

4. Pen Tool Chapter 8 The price, C, in dollars per share, of a high-tech stock has fluctuated over a 12-year period according to the equation C =14 +12x – x 2, where x is in years. The price, C, in dollars per share, of a second high-tech stock has shown a steady increase during the same time period according to the relationship C = –6 + 16x – x 2. For what value(s) are the two stock prices the same? Quadratic-Quadratic Systems The stock prices are the same at $49 at a time of 5 years. Solve the system using elimination.. Hint 1. Subtract the two equations 2. Solve the resulting equation 3. Determine the cost. Click here for the solution.

5. Pen Tool Homework Assignment: pgs 451 – 456: #s 1, 3abc, 5a, 10, 11, 13, 16, 19

6. Pen Tool The following pages contain solutions for the previous questions. Click here to return to the start

7. Pen Tool Solution 1. Subtract the two equations. 2. Solve the resulting equation. 3. Determine the cost for a time of 5 years. This can be verified graphically. The point of intersection of the two curves is (5, 49). Go back to the question. The stock prices are the same at 5 years and a price of $49.

8. Pen Tool For x = –3For x = – 4 The solutions are ( – 3, – 2) and ( – 4, 0) For ( – 3, – 2) For (–4, 0) Left Side Right Side Left Side = Right Side Right Side Solution Go back to the question. 1 2 2 1

9. Pen Tool The solutions are (3, 3) and (2, 1). Solution 1 2 Go back to the question. –