Systems of Linear Equations and Inequalities

2.3 Solving 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 = 64x – 6y = 42

(3, -5)

4x + 9y = 212x + 6y = 48

(5, -2)

Solving a Mixture application using the elimination methodJim 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 = 2250.21A + 0.30B = (0.24)225A = 150lbs b = 75lbs

Solve the system using the Elimination Method

x + 8y = -35-3x + 5y = -11

(-3, -4)

24d + 36g = 18014d + 20g = 96

(-6, 9)

Solve the following systems.5x – 7y = -4-3x + 9y = 6

( ¼, ¾)This is a consistent system with dependent lines. Any solution to the equation 2m-6n = -4 is also a solution to the system.

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

10x – 6y = 8Inconsistent no solution