TechMathI - 3.1 - Lines in Space Day3
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The document provides examples of solving systems of equations by elimination. It explains that to eliminate a variable, one should multiply one or both equations so they have the same coefficient in front of that variable. Then the equations should be added so that the terms with the variable to be eliminated cancel out, leaving an equation with only one variable that can be solved for. Four examples of this elimination method are shown and the reader is prompted to try solving additional example systems of equations on their own.
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TechMathI - 3.1 - Lines in Space Day3
- 1. Bell Ringer Find a line perpendicular to each. y = 3x - 1, (-1, -4) y = -2x + 12, (3, -9) m = ½x - 4, (2, 5)
- 2. Example 1: y = -5x + 12 y = -2x + 26 Example 2: y = -x - 12 y = -3x + 10 Find the intersection of the two lines:
- 3. You try! Example 1: y = 6x + 1 y = -4x + 10 Example 2: y = 12x - 6 y = -x + 1 Example 3: y = -x - 6 y = 2x - 3
- 4. Elimination Solving Systems of Equations
- 5. Multiply one or both equations so you have the same number in front of x or y. Look for opposites. Add the two equations. Solve for remaining variable. Example 1: 5x – 6y = -32 3x + 6y = 48
- 6. Multiply one or both equations so you have the same number in front of x or y. Look for opposites. Add the two equations. Solve for remaining variable. Example 2: 6x – 3y = 3 -6x + 5y = 3
- 7. Multiply one or both equations so you have the same number in front of x or y. Look for opposites. Add the two equations. Solve for remaining variable. Example 3: 2x + 3y = 11 -4x + y = -1
- 8. Multiply one or both equations so you have the same number in front of x or y. Look for opposites. Add the two equations. Solve for remaining variable. Example 4: 4x + 5y = 15 6x - 4y = 11
- 9. 3x + 2y = 6 x – 2y = 6 2x + 5y = -22 10x + 3y = 22 3x + 2y = -9 -10x + 5y = -5 You try!