Solving Systems of Equations by Elimination2

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Solving Systems of Equations by Elimination2 Name: Pd Algebra

{ { { Three ways to solve a system of equations: y = 2/5x – 2 y = -3x + 15 Graphing { 4x – 3y = 6 y = -3x + 15 Substitution { 5x + 3y = 3 2x – y = 6 Elimination

{ 5x + 2y = -16 Ex1: Solve the system by using elimination. Add systems + – 5x – 15y = -75 -13y = -91 -13 -13 { y = 7 5x + 2y = -16 1x + 3y = 15 -5( ) 1x + 3y = 15 Substitute the y 1x + 3(7) = 15 1x + 21 = 15 -21 -21 1x = -6 1 1 x = -6 Solution (-6, 7)

{ 6x + 3y = 9 Ex2: Solve the system by using elimination. Add systems = 10 10 10 { 3( ) x = 1 2x + y = 3 4x – 3y = 1 2x + 1y = 3 Substitute the x 2(1) + 1y = 3 2 + 1y = 3 -2 -2 1y = 1 1 1 y = 1 Solution (1, 1)

{ -6x – 12y = -60 Ex3: Solve the system by using elimination. Add systems + -5x + 12y = 82 -11x = 22 -11 -11 { x = -2 3( ) -2x – 4y = -20 -5x + 12y = 82 -5x + 12 y = 82 Substitute the x -5(-2) + 12y = 82 10 + 12y = 82 -10 -10 12y = 72 12 12 y = 6 Solution (-2, 6)

{ 15x + 5y = 10 Ex4: Solve the system by using elimination. Add systems + -15x – 9y = -18 -4y = -8 -4 -4 { y = 2 15x + 5y = 10 5x + 3y = 6 -3( ) 5x + 3y = 6 Substitute the x 5x + 3(2) = 6 5x + 6 = 6 -6 -6 5x = 0 5 5 x = 0 Solution (0, 2)

{ 8x – 10y = 6 Ex5: Solve the system by using elimination. Add systems + 15x + 10y = -75 23x = -69 23 23 { 2( ) x = -3 4x – 5y = 3 3x + 2y = -15 5( ) 3x + 2y = -15 Substitute the x 3(-3) + 2y = -15 -9 + 2y = -15 +9 +9 2y = -6 2 2 y = -3 Solution (-3, -3)

{ 16x + 12y = 76 Ex6: Solve the system by using elimination. = 76 Ex6: Solve the system by using elimination. Add systems + 9x – 12y = 24 25x = 100 25 25 { 4( ) x = 4 4x + 3y = 19 3x – 4y = 8 3( ) 4x + 3y = 19 Substitute the x 4(4) + 3y = 19 16 + 3y = 19 -16 -16 3y = -3 3 3 y = -1 Solution (4, -1)

{ 15x + 25y = -55 Ex7: Solve the system by using elimination. = -55 Ex7: Solve the system by using elimination. Add systems + -15x – 6y = 93 19x = 38 19 19 { 5( ) y = 2 3x + 5y = -11 5x + 2y = -31 3x + 5y = -11 -3( ) Substitute the x 3x + 5(2) = -11 3x + 10 = -11 -10 -10 3x = -21 3 3 x = -7 Solution (-7, 2)

{ -20x – 15y = 10 Ex8: Solve the system by using elimination. = 10 Ex8: Solve the system by using elimination. Add systems + 20x + 8y = -52 -7x = -42 -7 -7 { y = 6 5( ) -4x – 3y = 2 -5x – 2y = 13 -4x – 3y = 2 -4( ) Substitute the x -4x – 3(6) = 2 -4x – 18 = 2 +18 +18 -4x = 20 -4 -4 x = -5 Solution (-5, 6)

Sort your cards Sort your cards into 3 categories: No solution One Solution Infinitely many solutions