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Chapter 3 Lesson 2 Solving Systems of Equations Algebraically
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Vocabulary Substitution Method- One equation is solved for one variable in terms of the other, then that expression is substituted for the variable in the other equation Elimination Method- Eliminate one of the variables by adding or subtracting the equations
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Solutions Same as last section No Solutions When eliminating one variable, you eliminate the other and get an unequal equation, such as 0 = 2. One Solution Using substitution or elimination to get a single ordered pair as a solution. Infinitely Many Solutions When eliminating one variable, you eliminate the other and get an equal equation, such as 0 = 0.
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Substituting Pick one of the equations, does not matter which one Solve for a variable, usually the one that’s easiest to solve for Substitute what that variable equals in the other equation for that variable 2x+y=8 3y+4x=4 Top equation 2x+y=8 y=8-2x Substitute it into bottom equation 3(8-2x)+4x=4 2(10)+y=8 24-6x+4x=4 20+y=8 24-2x=4 y=-12 -2x=-20 x=10 Solution: (10,-12)
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Example 2r + s = 11 6r – 2s = -2
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Example 5a – b = 17 3a + 2b = 5
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Example 3s + 2t = -3 s + 1 / 3 t = -4
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Other Examples
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Elimination Subtracting one equation from the other to eliminate a variable 2x+3y=7 2(3)+3y=7 5x+3y=16 6+3y=7 3y=1 2x+3y=7 y= 1 / 3 -5x-3y=-16 __________ -3x=-9 x=3 Solution: (3, 1 / 3 )
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Example m – n = 9 7m + n = 7
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Example r + 4s = -8 3r + 2s = 6
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Example 6d + 3f = 12 2d= 8 - f
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Other Examples
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Homework Worksheet 3-2
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