Solving a System of Equations by Elimination Algebra Comprehensive October 31, 2011 Today is a B day!!!!

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Presentation transcript:

Solving a System of Equations by Elimination Algebra Comprehensive October 31, 2011 Today is a B day!!!!

Warm-up: (REVIEW OF PREVIOUS LESSONS) 1.) If the domain of the function f(x) = 2x 2 - 4x - 3 is [-3, 3], then what is the range? a.) [-5, 27] b.) [-3, 27] c.) [3, 27] d.) [5, 27] 2.) Solve the equation for x. 3(5x - 1) = 8 - 2x

Method of Elimination: When solving a linear system, you can sometimes add or subtract the equations to obtain a new equation in one variable. Steps to Solve Using the Elimination Method: Step 1: Add or Subtract the equations to eliminate a variable. Step 2: Solve the resulting equation for the other variable. Step 3: Substitute in either original equation to find the value of the eliminated variable.

Example 1: Using Addition to Eliminate a Variable 2x + 3y = 11 -2x + 5y = 13

Example 2: Using Subtraction to Eliminate a Variable 4x + 3y = -2 5x + 3y = -2

Example 3: Arranging Like Terms 8x - 4y = -4 4y = 3x + 14

Practice: 1.) 4x - 3y =52. 6x - 4y = 14 -2x + 3y = -7 -3x + 4y = x - 2y = 54. 2x + 5y = 12 7x - 3y = 4 5y = 4x + 6

Geometry Link: Th e rectangle has a perimeter P of 14 feet, and twice its length L is equal to 1 less than four times its width w. Write and solve a system of linear equations to find the length and the width of the rectangle.

Oil Change: Two cars get an oil change at the same service center. Each customer is charged a fee of x dollars for the oil change plus y dollars per quart of oil used. The oil change for the car that requires 5 quarts of oil costs $ The oil change for the car that requires 7 quarts of oil costs $ Find the fee and the cost per quart of oil.

Solve these systems of equations using addition or subtraction. x - y = 73x - 2y = 82x - 5y = -16 3x + y = 5x - 2y = 03y = 2x + 12 Suppose two eggs with bacon cost $2.70. One egg with bacon costs $1.80. At these rates, what will bacon alone cost? Five gallons of regular unleaded gas and eight gallons of premium gas cost $ Five gallons of regular unleaded and two gallons of premium gas cost $8.75. Find the cost per gallon of each kind of gasoline.

Homework: Pgs , 10, 15, 20, 23, 27, 38, and 41