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Warm-Up: September 20, 2012

Warm-Up: September 20, 2012. Write each equation in slope-intercept form (y = mx + b) = Solve for y x – y = 9 2x = 5y 4x + 7y = 14 3x – ½y = 6 2y + 8 = 6x. Any questions about functions?. Notes. Use graph paper for today’s notes Remember the Cornell Notes format.

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Warm-Up: September 20, 2012

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  1. Warm-Up: September 20, 2012 Write each equation in slope-intercept form (y = mx + b) = Solve for y x – y = 9 2x = 5y 4x + 7y = 14 3x – ½y = 6 2y + 8 = 6x

  2. Any questions about functions?

  3. Notes Use graph paper for today’s notes Remember the Cornell Notes format

  4. Solving Systems byGraphing or Substitution Section 3.1

  5. Essential Question How can we solve a system of two equations?

  6. System of Equations • A system of equations is two or more equations of the same variables. • Today, we will only deal with two equations / two variables. • For two equations / two variables, there are three possibilities: • One solution – the lines intersect • Infinite solutions – the lines are the same • No solutions – the lines are parallel

  7. The Three Possibilities

  8. Solving by Graphing • Write each equation in slope-intercept form (y = mx + b) • If both equations are the same, there are infinite solutions. • If both slopes are the same, but they have different y-intercepts, there are no solutions. • Otherwise, there is exactly one solution: • Graph each line • Find the coordinates of intersection (if they intersect) • Check your answer by substituting into both original equations.

  9. Example 1: Page 161 #15 y = 2x – 1 6x – y = 13

  10. You-Try #1: Page 161 #21 4x + 5y = -7 3x – 6y = 24

  11. Assignment

  12. Warm-Up: September 21, 2012 Evaluate each of the following:

  13. Solving by Substitution Solve one equation for one variable. Substitute the expression for that variable into your other equation. Solve for the remaining variable. Substitute the value into either original equation to solve for the other variable. Check your answer by substituting into the other equation.

  14. Example 2: Page 161 #29 x – 2y = 0 2x – y = 6

  15. You-Try #2: Page 161 #27 4x + 2y = 20 y = x – 2

  16. Assignment • Page 161 #13-35 odd • 8 new problems

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