Systems of Linear Equations and Inequalities 2.3Solving Systems of Equations Using the Elimination Method Solve a system of equations using the elimination.

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Presentation transcript:

Systems of Linear Equations and Inequalities 2.3Solving Systems of Equations Using the Elimination Method Solve a system of equations using the elimination method. Solve applications using systems of equations and the elimination method.

Elimination Method for Solving Systems of Equations Used best when both equations are in general form or when no variable is already isolated or easily isolated. Multiply one or more of the equations by a number to make the coefficients of one variable opposite in sign but of the same value. Add the two equations to eliminated the variable, then solve. Remember to find the values for both variables. Check the solution in both equation.

Solve the system using the Elimination Method 7x + 3y = 6 4x – 6y = 42 (3, -5) 4x + 9y = 2 12x + 6y = 48 (5, -2)

Solving a Mixture application using the elimination method Jim Johnson is a local veterinarian who has prescribed a diet of 24% protein for a client’s Great Dane. Jim has the two types of dog food shown below, but neither is 24% protein. The client wants 225 pounds of food to feed the great Dane until the next vet appointment. How much of each type of food should Jim sell his client. A = The amount of 21% protein dog food used. B = The amount of 30% protein dog food used. A + B = A B = (0.24)225 A = 150lbsb = 75lbs

Solve the system using the Elimination Method x + 8y = x + 5y = -11 (-3, -4) 24d + 36g = d + 20g = 96 (-6, 9)

Solve the following systems. 5x – 7y = -4 -3x + 9y = 6 ( ¼, ¾)

Solve the following systems. 15x + 14y = 16 -3x + 21 y = 7 ( 2/3, 3/7)