Systems of Equations Solve by Graphing.

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Systems of Equations Solve by Graphing

Graph both linear equations on the same graph y = x – 2 y x x y 1 2 -2 -1 y = -2x + 1 Solution (1,-1) x y 1 2 (1, -1) 1 -1 -3

Graph both linear equations on the same graph y = 4x + 3 y x x y -1 -2 3 -1 -5 y = -x - 2 (-1,-1) Solution x y 1 2 (1, -1) -2 -3 -4

Systems of Equations Solve by Substitution

x + 3y = 20 x = 4 + 5y x = 4 +5y x = 4 +5(2) x = 4 +10 4 + 5y + 3y = 20 8y + 4 = 20 x = 14 8y = 16 Solution (14,2) y = 2

2x + y = 20 y = -2x + 20 y = -2x + 20 6x - 5y = 12 y = -2(7) + 20 Solution (7,6) x = 7

Systems of Equations Solve by Elimination

Solve the System of Equations 2x + 4y = 40 2x + 4y = 40 -2x - y = -16 2x + 4(8) = 40 2x + 32 = 40 0x + 3y = 24 2x = 8 3y = 24 y = 8 x = 4 Solution (4, 8)

Solve the System of Equations These need to have the same coefficient [ ] 2x + y = 20 10x + 5y = 100 (5) = 6x - 5y = 12 6x -5 y = 12 16x + 0y = 112 16x = 112 6x - 5y = 12 x = 7 6(7) - 5y = 12 42 - 5y = 12 -5y = -30 y = 6 Solution (7, 6)