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Solving Systems of Linear Equations by Substitution
Session 5Practice Test – Sept 13LT # 2 – Sept 15
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ObjectivesChoose the appropriate
variable to solve for in a given system of equations.
Solve systems of linear equations by the substitution method.
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RECALL: Solve by graphing.
Identifying the point of intersection may produce inaccurate results.
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SUBSTITUTION
Replacing one variable so that there is only one variable to solve for instead of two.
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What variable is isolated on one side of the equation?
2x – 5(x + 7) = 4
Substitute x + 7 in (1).
(1)
(2)
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2x – 5(x + 7) = 42x – 5x – 35 = 4 -3x = 4 + 35 -3x = 39 x = -13y = x + 7 = -13 + 7 = -6
(-13, -6)
How do we know if the values of x and y are correct?
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2x – 5y = 4 (1) y = x + 7 (2)
How do we know if the values of x and y are correct?
(-13, -6)
2(-13) -5(-6) = 4
-26 + 30 = 4
4 = 4
-6 = -13 + 7
-6 = -6
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What variable has a coefficient or either 1 or -1. Rewrite each equation to isolate the variable.
If we make x the subject of the equations, will we get the same solution? Which way is it easier?
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What variable has a coefficient or either 1 or -1. Rewrite each equation to isolate the variable.
If we make y the subject of the equations, will we get the same solution? Which way is it easier?
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Which variable has the smallest integral coefficient? Isolate this variable on one side of the equation.
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How to choose which variable to solve for
1. A variable is already isolated on one side of the equation.
ex. 2x – 5y = 4 y = x + 7
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How to choose which variable to solve for
2. One of the variables has a coefficient of 1 or -1.
ex. 2x + 6y = 3 x – 4y = 2
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How to choose which variable to solve for
3. Choose the variable with the smallest integer coefficient.
ex. 11x – 7y = 10 14x + 2y = 9
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How to identify systems that have no solution and that have more than one solution
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SYSTEMS THAT HAVE NO SOLUTION(Inconsistent)
2x – 3y = 66x – 9y = 36
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9x + 6y = 66x + 4y = 4
SYSTEMS THAT HAVE MORE THAN ONE SOLUTION(Consistent, Dependent)
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SeatworkExercise 5c # 1, a – e NSM Book 2 page 163
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(a) x + y = 7x – y = 5
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b) 3x – y = 02x + y = 5
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c) 2x – 7y = 53x + y = -4
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d) 5x – y = 53x + 2y = 29
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e) 5x + 3y = 114x – y = 2
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HomeworkExercise 5c page 163, number 1 f – j
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For further understanding http://www.youtube.com/watch?v=PIzV_
NYkhUM&feature=relmfu http://www.regentsprep.org/Regents/ma
th/ALGEBRA/AE3/AlgSys.htm http
://teachers.henrico.k12.va.us/math/hcpsalgebra1/Documents/examviewweb/ev9-2.htm