Solving System of Linear Equations Elimination Method Warmup

Solving System of Linear Equations Elimination Method

Warm-up: solve the linear system by Elimination y - 2 x = -3 y - x = -1 (2, 1)

Multiplying one equation (5)( -2 x - 5 y = 22 )(5) 10 x + 3 y = 22 -10 x - 25 y = 110 10 x + 3 y = 22 0 - 22 y = 132 -22 y = -6 -2 x - 5 y = 22 -2 x - 5(-6) = 22 -2 x + 30 = 22 - 30 -2 x -2 = -8 -2 x=4 (4, -6)

Your turn! 4 x + 2 y = -10 (2)( -2 x + 3 y = 33 )(2) 4 x + 2 y = -10 -4 x + 6 y = 66 0 + 8 y = 56 8 8 y=7 4 x + 2 y = -10 4 x + 2(7) = -10 4 x + 14 = -10 - 14 4 x 4 = -24 4 x = -6 (-6, 7)

Your turn… 4 x + 10 y = 70 again! 2 x - 5 y = 25 -2(2 x 25) 4 x + 10 y = 70 -4 x + 10 y = -50 20 y = 20 20 = 20 y = 1 4 x + 10 y = 70 -4 x + 10 y = -50 4 x + 10 y = 70 4 x + 10(1) = 70 4 x + 10 -10 4 x 4 x = 70 = -10 = 20 4 = 5 Answer: (5, 1)

Practice! Hint: multiply the first equation by 4 2 x - y = 9 3 x + 4 y = -14 Answer: ( 2, -5 )

Multiplying two equations (5)( 3 x + 5 y = 10 )(5) (-3)( 5 x + 7 y = 10 )(-3) 15 x + 25 y = 50 -15 x - 21 y = -30 0 + 4 y = 20 4 4 y=5 3 x + 5 y = 10 3 x + 5(5) = 10 3 x + 25 = 10 - 25 3 x 3 = -15 3 x = -5 (5, -5)

Your Turn! (3)( 2 x - 3 y = -11 )(3) (-2)( 3 x + 2 y = 29 )(-2) 6 x - 9 y = -33 -6 x -4 y = -58 0 -13 y = -91 -13 y=7 2 x - 3 y = -11 2 x - 3(7) = -11 2 x - 21 = -11 + 21 +21 2 x 2 = 10 10 x=5 (7, 5)

Summary: On Solving Linear Systems (Graphing, Substitution, Elimination Methods) Graphing: 1. ) y = 2 x - 3 y = -3 x + 2 2. )y = y= ½x + 1 -⅔x 3. ) y = y= -½x + 1 -5 x -1 Substitution 1. ) 2 x + y = 8 y=x-7 Elimination 1. ) x + 2 y = 7 3 x - 2 y = 1 2. ) y = 3 x - 6 -3 x + y = -6 3. ) y = x + 4 y = 3 x 2. ) 8 x - 9 y = 19 4 x + y = -7 3. ) 4 x - 3 y = 11 3 x - 5 y = -11

Classwork 1. ) 8 x + 11 y = 20 5 x - 11 y = -59 2. ) 2 x - 3 y = 61 2 x + y = -7 3. ) 2 x - 3 y = 5 x + 2 y = -1 4. ) 20 x + 3 y = 20 -20 x + 5 y = 60