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Solving Systems of Equations The Method of Elimination. Hi Class, Sorry I’m not there, but my son is sick. Try your best to follow and copy these slides. This is a new method for finding the Point of Intersection (POI). Solving by Elimination Example: 2x + y = 10 and 4x + y = 2.
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Solving Systems of Equations The Method of Elimination
Hi Class, Sorry I’m not there, but my son is sick. Try your best to follow and copy these slides. This is a new method for finding the Point of Intersection (POI)
Solving by Elimination Example: 2x + y = 10 and 4x + y = 2 Step 1: Line up the equations on top of each other and draw a line underneath. 2x + y = 10 Step 2 – Choose to add or subtract the 2 equations. *The point is to eliminate (get rid of) the x’s or the y ‘s. 4x + y = 2 So, it makes sense to SUBTRACT these equations and eliminate the y’s. Note: If you added the equations, neither the x’s or the y’s would disappear. So……
So….place a subtraction sign in front of the second equation and subtract the x’s and the y’s 2x + y = 10 -- 4x + y = 2 -2x = 8 x = 8/-2 x = -4 Now, divide both sides by -2 to isolate x Next….find y (substitute x = -4 back into one of the original equations) 2x + y = 10 2(-4) + y = 10 -8 + y = 10 y = 10 + 8 y = 18 Therefore the POI is (- 4, 18)
X + 2y = 2 X – 2y = 4 __ Should we add or subtract? **YOU have to CHOOSE the x or y to eliminate. If we choose the x’s to eliminate, then we should subtract 4y = -2 Y = -0.5 Now find x by substituting y=-0.5 into either of the first two equations. X + 2(-0.5) = 2 X –1 = 2 X = 3 The solution is (3, -0.5)
x + y = 1/2 2x – y = 5/2 + Should we add or subtract? **Note: if we subtract, nothing would be eliminated 3x = 3 x = 1 Now find y by substituting x=1 into either of the first two equations. x + y =1/2 1 + y = ½ y = ½ -1 y= -0.5 The solution is (1, -0.5)
x + y = 3 x – y = 7 __ Should we add or subtract? Again: YOU CHOOSE the x or y to eliminate. In this question I chose to eliminate x. Soooo……I have to SUBTRACT 2y = -4 y = -2 Now find x by substituting y=-2 into either of the first two equations. x + y = 3 x + (-2) = 3 x –2 = 3 x = 3 + 2 x = 5 The solution is (5, -2)
x - y =1 2x + y = 5 + Should we add or subtract? 3x = 6 x = 2 Now find y by substituting x = 2 into either of the first two equations. x – y = 1 2 – y = 1 -y = 1 - 2 -y = -1 y = -1 The solution is (2, 1)
Homework Handout: The Elimination Method (Day 1)