Classification of solutions
- 1. Housekeeping
- 2. Unit 2: Lesson 7 Classification of Solutions • Students know the conditions for which a linear equation will have a unique solution, no solution, or infinitely many solutions.
- 3. A solution to an equation is a value you can substitute in for the variable that makes the equation true.
- 4. Did you know that some equations have more than one solution or no solution?
- 5. Consider the following equation: 2(x + 1) = 2x − 3. What value of x makes the equation true?
- 6. Solve each of the following equations for x. 1. 7x – 3 = 5x + 5 2. 7x – 3 = 7x + 5 3. 7x – 3 = -3 + 7x
- 7. Solve each of the following equations for x. 1. 7x – 3 = 5x + 5
- 8. Solve each of the following equations for x. 2. 7x – 3 = 7x + 5
- 9. Solve each of the following equations for x. 3. 7x – 3 = - 3 + 7x
- 10. 7x – 3 = 5x + 5 7x – 3 = 5x + 5 7x – 3 = - 3 + 7x
- 11. X + 5 = 8 10 = 2x 2X = X One Solution Equations! x + 1 = x + 4 No Solution Equations! 2x + 3 = 2x + 5 variable terms: same constants: different variable terms: on one side or different constants: same or different
- 12. 7y = 7y PENCILS PENCILS = = Identity equations are equations that are true no matter what value is plugged in for the variable. If you simplify an identity equation, you'll ALWAYS get a true statement.
- 13. variable terms: same constants: same identity statement = infinite solutions
- 14. variable terms: same constants: same variable terms: same constants: different One Solution No Solution Infinite Solutions variable terms: usually only one constants: different
- 15. Give a brief explanation as to what kind of solution(s) you expect the following linear equations to have. Transform the equation into a simpler form if necessary. 11x – 2x + 15 = 8 + 7 + 9x
- 16. Give a brief explanation as to what kind of solution(s) you expect the following linear equations to have. Transform the equation into a simpler form if necessary. 3(x-14) + 1 = -4x + 5
- 17. Give a brief explanation as to what kind of solution(s) you expect the following linear equations to have. Transform the equation into a simpler form if necessary. -3x + 32 – 7x = -2(5x + 10)
- 18. Give a brief explanation as to what kind of solution(s) you expect the following linear equations to have. Transform the equation into a simpler form if necessary. 1 2 8𝑥 + 26 = 13 + 4𝑥
- 19. Write two equations that have no solution
- 20. Write two equations that have one unique solution each
- 21. Write two equations that have infinitely many solutions
- 22. • We know that equations will either have a unique solution, no solution, or infinitely many solutions. • We know that equations with no solution will, after being simplified on both sides, have coefficients of x that are the same on both sides of the equal sign and constants that are different. • We know that equations with infinitely many solutions will, after being simplified on both sides, have coefficients of x and constants that are the same on both sides of the equal sign. IXL Skill U.12