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Thursday Warmup Homework Check: Document Camera

SWBAT solve systems of equations by elimination. Math 1B Unit 0 Day 7 Objective: SWBAT solve systems of equations by elimination.

Solving Systems Using Elimination Obj: To solve systems by adding or subtracting. Elimination Method: A method for solving a system of linear equations. You add or subtract the equations to eliminate a variable.

Ex 1: Solve by elimination. 2x + 3y = 11 Step 1: Eliminate x because the sum of the coefficients is 0. 2x + 3y = 11 –2x + 9y =1 0 + 12y = 12 Addition Property of Equality y = 1 Solve for y. Step 2: Solve for the eliminated variable x using either original equation. 2x + 3y = 11 Choose the first equation. 2x + 3(1) = 11 Substitute 1 for y. 2x + 3 = 11 Solve for x. 2x = 8 x = 4

Ex 1 (continued) Since x = 4 and y = 1, the solution is (4, 1). Check: See if (4, 1) makes true the equation not used in Step 2. –2(4) + 9(1) 1 Substitute 4 for x and 1 for y into the second equation. –8 + 9 1 1 = 1

Ex 2: On a special day, tickets for a minor league baseball game were $5 for adults and $1 for students. The attendance that day was 1139, and $3067 was collected. Write and solve a system of equations to find the number of adults and the number of students that attended the game. Define: Let a = number of adults Let s = number of students Relate: total number at the game total amount collected Write: a + s = 1139 5 a + s = 3067 Solve by elimination.

Ex 2 (continued) Step 1: Eliminate one variable. a + s = 1139 5a + s = 3067 –4a + 0 = –1928 Subtraction Property of Equality a = 482 Solve for a. -( ) Step 2: Solve for the eliminated variable using either of the original equations. a + s = 1139 Choose the first equation. 482 + s = 1139 Substitute 482 for a. s = 657 Solve for s. There were 482 adults and 657 students at the game. Check: Is the solution reasonable? The total number at the game was 482 + 657, or 1139. The money collected was $5(482), or $2410, plus $1(657), or $657, which is $3067. The solution is correct.

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