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Solving Equation Systems Every Way!

Solving Equation Systems Every Way!. Thursday, Feb 13 th. Solving by Graphing. The main idea: Rearrange each equation for y Find the slope and intercepts Graph both lines Identify where the two lines intersect. Solving by Graphing.

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Solving Equation Systems Every Way!

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  1. Solving Equation Systems Every Way! Thursday, Feb 13th

  2. Solving by Graphing The main idea: • Rearrange each equation for y • Find the slope and intercepts • Graph both lines • Identify where the two lines intersect

  3. Solving by Graphing In your teams, solve the following system of equations by graphing: y = 3x + 1 y = ½x + 6 2y + 3x = 6 y = ½x – 5 Extra challenge: 4x - 7y = 0 ¾x + 5y = 8

  4. Solving by Graphing Solutions: y = 3x + 1 y = ½x + 6 2y + 3x = 6 y = ½x – 5 (4, -3) (2, 7)

  5. Solving by Substitution The main idea: • Rearrange one equation for y • Plug this in to replace y in the second equation • Solve for x • Plug x back into the first equation to get y

  6. Solving by Substitution In your teams, solve the following systems of equations by substitution: y = 4x - 5 -3y + 7x = 35 2y + 9x = 7 -12x – 4y = -2 Extra challenge: 8x – ¾y = 1 2x + ½y = 7

  7. Solving by Elimination The main idea: • Write the two equations on top of each other, lining up x’s and y’s and constants • Add or subtract the equations to eliminate one variable (x or y) • Solve for the remaining variable • Plug back into the first equation to get the other variable

  8. Solving by Elimination In your teams, solve the following systems of equations by elimination: 5y + 6x = 3 9y – 6x = 11 7y – ¼x = 6 7y – ¾x = -4 Extra challenge: 8x – ¾y = 1 2x + ½y = 7

  9. Where is this math handy for real life? Jarrod is designing an backyard ice rink for some hockey, and he wants the length to be 1.5 times the width. He borrows 100m length of 2x4 boards from Erica’s family to line the outside of the ice rink. What should Jarrod make the length and width of his ice rink to maximize it’s area without needing to borrow more boards?

  10. Your turn! Homework: Turning real-life scenarios into solvable equations • Page 36 #3 – 5 • Page 37 Part 2: #2, Part 3: #2, 3 Due tomorrow: create one word problem (it can be goofy!) that requires the reader to create and solve two equations. We will trade problems and solve tomorrow.

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