Myp10 system of linear equations with solution

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solve system of linear equations by graphing, elimination and substitution (review)

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Myp10 system of linear equations with solution

  1. 1. System of Linear Equations MYP 10 ­ CIC
  2. 2. What is a system of equation? A system of equations just means ­ more than 1 equation more than 1 variable (x & y) more than 1 line 
  3. 3. What is the solution of a system of linear equations? The solution is where the equations meet       or intersect.
  4. 4. How many solutions can a system of linear equations have? Case 1:  1 solution
  5. 5. How many solutions can a system of linear equations have? Case 2:  no solution
  6. 6. How many solutions can a system of linear equations have? Case 3:  infinite solutions
  7. 7. How can we find solutions to the system of equations? 1) Solve by graphing 2) Solve by elimination 3) Solve by substitution
  8. 8. Elimination Method 2x – y = 1 3x + y = 9 We have the same number of  y’s in each If we ADD the equations, the y’s disappear+ 5x = 10 Divide both sides by 5 x = 2 A B Substitute x = 2 in equation A 2 x 2 – y = 1 4 – y = 1 y = 3 Answer x = 2, y = 3
  9. 9. Substitution Method 2x – y = 1 3x + y = 9 A B y = −3x + 9 2x −(−3x + 9) =1substitute 2x +3x − 9 =1 5x − 9 =1 5x =10 x = 2 3(2)+ y = 9 6+ y = 9 y = 9 − 6 y = 3
  10. 10. Graphing Method 2x – y = 1 3x + y = 9 A B 2x – 1 = y y = -3x + 9 (2, 3)
  11. 11. Solve 3x - 2y = 7 5x + 3y = 37 + 19x = 95 In B A B 5 x 5 + 3y = 37 3y = 12 y = 4 Answer x = 5, y = 4 Multiply A by 3 & B by 2, we get +6y & -6y 9x – 6y = 21 10x + 6y = 74B A x = 5 Could multiply A by 5 & B by 3 to get 15x in each
  12. 12. Solve
  13. 13. Solution: a)(2, 5) b)(3, 1) c)(2, 4/3) d)(2, -2) e)(-3, 4) f)(2, -3) g)Infinite solutions h)No solutions

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