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

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- 1. System of Linear Equations MYP 10 CIC
- 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. What is the solution of a system of linear equations? The solution is where the equations meet or intersect.
- 4. How many solutions can a system of linear equations have? Case 1: 1 solution
- 5. How many solutions can a system of linear equations have? Case 2: no solution
- 6. How many solutions can a system of linear equations have? Case 3: infinite solutions
- 7. How can we find solutions to the system of equations? 1) Solve by graphing 2) Solve by elimination 3) Solve by substitution
- 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. 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. Graphing Method 2x – y = 1 3x + y = 9 A B 2x – 1 = y y = -3x + 9 (2, 3)
- 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. Solve
- 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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