Warmups – solve using substitution

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Warmups – solve using substitution y = x + 4 2. 4x + y = 0 3x – 2y = -7 2y + x = -7 Solve by graphing: x + y = 3 2x + 2y = -6

Substitution: Special Cases x + y = 16 x = 16 – y 2y = -2x + 2 2y = -2(16 – y) + 2 2y = -32 + 2y + 2 2y = -30 + 2y 0 = -30 False NO SOLUTION 6x – 2y = -4 y = 3x + 2 6x – 2(3x + 2) = -4 6x – 6x – 4 = -4 -4 = -4 True INFINITELY MANY

8-3 Elimination Using Addition Objective: To solve systems of equations using the elimination method.

Example 1 3x – 2y = 4 4x + 2y = 10 + 4x + 2y = 10 7x + 0y = 14 7x = 14 x = 2 Substitute! Rows 1-3: Use first equation Rows 4-5: Use second equation Answer: (2,1)

Try with an allstar 1) -3x + 4y = 12 2) x + y = 8 3x – 6y = 18 x – y = 4 (-24,-15) (6,2)

Example 2 x + y = 18 x + 2y = 25 Multiply an equation by (-1) x + y = 18 + -x – 2y = -25 0x – y = -7 -y = -7 y = 7 Substitute! x + 7 = 18 x = 11 -1(x + 2y = 25) -x – 2y = -25 Answer: (11,7)

TOO 1) 13x + 5y = -11 2) 3x – 5y = -35 13x + 11y = 7 2x – 5y = -30 (-2,3) (-5,4)

Remember . . . 0 = 10 0 = 0 No Solution Infinitely Many 0 = 10 0 = 0 No Solution Infinitely Many TOO for Homework x + y = 7 2) 3x + y = 5 3) 2x – 5y = -6 x + y = 11 2x + y = 10 -2x + 7y = 14

Homework Pg. 473 #15-30 Left Column