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

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Solve Linear Systems by Elimination February 3, 2014 Pages

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.

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).

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 x – 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).

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).

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–

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

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

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.

HOMEWORK PAGE 447, # 4-22, EVEN