Tham khảo tài liệu 'number operation review 10', ngoại ngữ, anh ngữ phổ thông phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | ------------------------------------- ALGEBRA REVIEW ------------------------------------------- c 2d 13 c 2 11 - 2c 13 c 22 - 4c 13 22 - 3c 13 22 13 3c 9 3c c 3 Now substitute this answer into either original equation for c to find d. 2c d 11 2 3 d 11 6 d 11 d 5 Thus c 3 and d 5. Linear Combination Linear combination involves writing one equation over another and then adding or subtracting the like terms so that one letter is eliminated. Example x 7 3y and x 5 6y First rewrite each equation in the same form. x 7 3y becomes x 3y 7 x 5 6y becomes x 6y 5. Now subtract the two equations so that the x terms are eliminated leaving only one variable x 3y 7 x 6y 5 x x 3y 6y 7 5 3y 12 y 4 is the answer. Now substitute 4 for y in one of the original equations and solve for x. x 7 3y x - 7 3 4 x - 7 12 x - 7 7 12 7 x 19 Therefore the solution to the system of equations is y 4 and x 19. 89 -------------------------------------- ALGEBRA REVIEW ---------------------------------------------- Systems of Equations with No Solution It is possible for a system of equations to have no solution if there are no values for the variables that would make all the equations true. For example the following system of equations has no solution because there are no values of x and y that would make both equations true 3x 6y 14 3x 6y 9 In other words one expression cannot equal both 14 and 9. Practice Question 5x 3y 4 15x dy 21 What value of d would give the system of equations NO solution a. 9 b. -3 c. 1 d. 3 e. 9 Answer e. The first step in evaluating a system of equations is to write the equations so that the coefficients of one of the variables are the same. If we multiply 5x 3y 4 by 3 we get 15x 9y 12. Now we can compare the two equations because the coefficients of the x variables are the same 15x 9y 12 15x dy 21 The only reason there would be no solution to this system of equations is if the system contains the same expressions equaling different numbers. Therefore we must choose the .
