1. Solve Linear Systems by Elimination February 3, 2014 Pages 444-446

2. 7.3 SOLVING SYSTEMS BY ELIMINATION Students will be able to: Solve systems of linear equations in two variables by elimination. Compare and choose an appropriate method for solving systems of linear equations.

3. 1. Solve the linear system by elimination. 2x + 3y = 11 – 2x + 5y = 13 Equation 1 Equation 2 SOLUTION Add the equations to eliminate one variable. 2x + 3y = 11 – 2x +5y = 13 Solve for y. 8y = 24 y = 3 Substitute 3 for y in either equation and Solve for x. STEP 1 STEP 2 STEP 3 2x + 3y = 11 Write Equation 1 2x + 3(3) = 11 Substitute 3 for y. x = 1 Solve for x. ANSWER The solution is (1, 3).

4. 2. Solve the linear system by elimination. 8x – 4y = –4 Equation 1 4y = 3x + 14 Equation 2 SOLUTION STEP 1 Rewrite Equation 2 in standard form. 8x – 4y = –4 4y = 3x + 14 8x – 4y = –4  3x + 4y = 14 STEP 2 Add the equations. 5x = 10 STEP 3 Solve for x. x = 2 STEP 4 Substitute 2 for x in either equation and solve for y. 4y = 3x + 14 Write Equation 2. 4y = 3(2) + 14 Substitute 2 for x. y = 5 Solve for y. ANSWER The solution is (2, 5).

5. 3. Solve the linear system by elimination. 4x – 3y = 5 – 2x + 3y = – 7 Equation 1 Equation 2 SOLUTION Add the equations to eliminate one variable. 4x – 3y = 5 – 2x +3y = – 7 Solve for x. 2x = – 2 x = – 1 Substitute – 1 for x in either equation and Solve for x. STEP 1 STEP 2 STEP 3 4x – 3y = 5 Write Equation 1. 2(– 1) – 3y = 5 Substitute – 1 for x. y = – 3 Solve for x. ANSWER The solution is (– 1, – 3).

6. 4. Solve the linear system by elimination. Equation 1 5x + 2y = 4 Equation 2 SOLUTION Add the equations to eliminate one variable. Solve for y. – 4y = 12 Substitute – 3 for y in either equation and solve for y. STEP 1 STEP 2 STEP 3 y = – 3 5x – 6y = 8– 5x + 2y = 4 5x – 6y = 8– Write Equation 1. Substitute – 3 for y. x = 2 Solve for x. ANSWER The solution is (2, -3). 5x – 6y = 8– 5x – 6(–3) = 8–

7. 5. Solve the linear system by elimination. Equation 1 Equation 2 SOLUTION Add the equations to eliminate one variable. Solve for x. Substitute 5 for x in either equation and solve for y. STEP 1 STEP 2 STEP 3 x = 5 6x – 4y = 14 3x + 4y = 1 – 6x – 4y = 14 3x + 4y = 1 – 3x = 15 Write Equation 1. Substitute 5 for x. y = 4 Solve for y. ANSWER The solution is (5, 4). 6x – 4y = 14 6(5) – 4y = 14

8. 6. Solve the linear system by elimination. Equation 1 Equation 2 SOLUTION STEP 1 Rewrite Equation 2 so that the like terms are arranged in columns. STEP 2 Subtract the equations. STEP 3 Solve for x. x = 1 2x + 5y = 12 = 4x + 6 5y5y 2x + 5y = 12 – 4x + 5y = 6 2x + 5y = 12 = 4x + 6 5y5y 6x = 6

9. Write Equation 2. Substitute 1 for x. x = 2 Solve for y. ANSWER The solution is (1, 2). + 5y = 6 2(1) 2x + 5y = 12 STEP 4 Substitute 1 for x in either equation and solve for y.

10. HOMEWORK PAGE 447, # 4-22, EVEN