1. Solving Systems of Equations by Elimination Name: Pd Algebra 3/03/09

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

3. -3x – 5y = 23 2x + 5y = -27 -3x – 5y = 23 2x + 5y = -27 + -1x= -4 x = 4 -3x – 5y = 23 -3(4) – 5y = 23 -12 – 5y = 23 +12 -5y= 35 -5 y = -7 Ex1: Solve the system by using elimination. { Solution (4, -7) Add systems Substitute the x

4. x + 4y = -36 -5x – 4y = 52 1x + 4y = -36 -5x – 4y = 52 + -4x= 16 -4 x = -4 1x + 4y = -36 1(-4) + 4y = -36 -4 + 4y = -36 +4 4y= -32 44 y = -8 Ex2: Solve the system by using elimination. { Solution (-4, -8) Add systems Substitute the x

5. 2x – 3y = -9 -2x + 3y = 10 2x – 3y = -9 -2x + 3y = 10 + 0= 1 Is this true? Ex3: Solve the system by using elimination. { No solutions Add systems No!

6. 2x + 5y = -57 -2x + 5y = -33 2x + 5y = -57 -2x + 5y = -33 + 10y= -90 10 y = -9 2x + 5y = -57 2x + 5(-9) = -57 2x – 45 = -57 +45 2x= -12 2 2 x = -6 Ex4: Solve the system by using elimination. { Solution (-6, -9) Add systems Substitute the y

7. { -2x – 2y = 12 3x – 2y = -33 2x 3x – 2y = -33 + 5x= -45 5 5 x = -9 3x – 2y = -33 3(-9) – 2y = -33 -27 – 2y = -33 +27 -2y= -6 -2 y = 3 Ex5: Solve the system by using elimination. Solution (-9, 3) Add systems Substitute the x -1 ( ) + 2y= -12

8. – 4y { -x + 4y = 2 -x + y = -1 1x -1x + 1y = -1 + -3y= -3 -3 y = 1 -1x + 1y = -1 -1x + 1(1) = -1 -1x + 1 = - 1 -1x= -2 x = 2 Ex6: Solve the system by using elimination. Solution (2, 1) Add systems Substitute the y -1 ( ) = -2

9. + 3y { 4x – 3y = 8 4x – 3y = 8 -4x 4x – 3y = 8 + 0= 0 Is this true? Ex7: Solve the system by using elimination. Infinite Solutions Add systems Yes! -1 ( ) = -8

10. – 4y { 2x + 4y = -8 x + 4y = -18 -2x 1x + 4y = -18 + -1x = -10 x = 10 x + 4y = -18 10 + 4y = -18 -10 4y= -28 4 4 y = -7 Ex8: Solve the system by using elimination. Solution (10, -7) Add systems Substitute the x -1 ( ) = 8

11. -3x + 3y = 6 3x + 5y = -30 -3x + 3y = 6 3x + 5y = -30 + 8y= -24 8 8 y = -3 3x + 5y = -30 3x + 5(-3) = -30 3x – 15 = -30 +15 3x= -15 3 3 x = -5 Ex9: Solve the system by using elimination. { Solution (-5, -3) Add systems Substitute the y

12. 3(2y + 6) + 2y = 10 3x + 2y = 10 x = 2y + 6 { 6y+ 18+ 2y 8y+ 18 = 10 -18 8y = -8 8 8 y = -1 = 10 x = 2y + 6 x = 2(-1) + 6 x = 4 Solution: (4, -1) x, y Use substitution to solve systems.

13. Complete your classwork packet, it will be collected at the end of class for a grade If you finish early you may complete the exit ticket and pick up your homework