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3 Cards in this Set
- Front
- Back
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What is the Subsitution Method for solving systems of linear equations.
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The subsitution method is an algebraic method for solving a system of equations in which one equation is solved for the variables and the result is subsituted into the other equation.
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Systems of equations that are parallel lines
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(1) x = 5 - 2y
(2) 2x + 4y = 6 2x + 4y = 6 2(5 - 2y) + 4y = 6 10 - 4y + 4y = 6 10 = 6 False The false result means that the equations in the systems have graphs that are parallel lines. The system in inconsistent and has no solution. The solution set is 0 with a slash. Caution: It is common error to give "false" as the solution of an inconsistent system. The correct reponse is 0 with a slash. |
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Systems of equations that are dependent equations (have the same graph)
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(1) 3x - y = 4
(2) -9x + 3y = -12 Solve Equation 1 for y to get y = 3x - 4. Subsitute 3x - 4 for y in equation (2) and solve the resulting equation. -9x + 3y = -12 -9x + 3 ( 3x - 4 ) = -12 -9x + 9x - 12 = -12 -12 = -12 0 = 0 This true results means that every solution of one equation is also a solution of the other, so the system has an infinite number of solutions. The solution set is {(x,y)| 3x -y= 4}. Caution: It is a common error to give "true" as the solution of a system of dependent equations. Remember to give the solution set in set-builder notation using trhe equation in the system that is in standard form with integer coefficients that have no common factor (except 1). |
