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Bellwork

Bellwork. Solve the system 2x+3y=-9 x-2y=6 You buy 8 pencils for $8 at the bookstore. Standard pencils cost $.85 and specialty pencils cost $1.25. How many specialty pencils did you buy?. Example. Solve the system 2x+3y=-9 x-2y=6. Example.

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Bellwork

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  1. Bellwork • Solve the system • 2x+3y=-9 x-2y=6 • You buy 8 pencils for $8 at the bookstore. Standard pencils cost $.85 and specialty pencils cost $1.25. How many specialty pencils did you buy?

  2. Example • Solve the system • 2x+3y=-9 x-2y=6

  3. Example You buy 8 pencils for $8 at the bookstore. Standard pencils cost $.85 and specialty pencils cost $1.25. How many specialty pencils did you buy?

  4. Solve Special Types of Linear Systems Section 7.5

  5. The Concept • Since discussing linear systems, we’ve created a quiver of methods for solving: Graphing, Substitution and Elimination • Today we’re going to talk about some special kinds of systems

  6. Vocabulary • Inconsistent System • A system of equations in which no point of intersection exists • These lines are Parallel • Consistent System • A system of equations in which all solutions to both equations serve as solutions to the other • These systems have infinitely many solutions • They are in fact the same lines

  7. Example Let’s do an example 5y+1x=9 5y=-x+13

  8. Example Let’s do an example 2y+2x=12 x=-y+6

  9. Findings • If lines are parallel, then they will never intersect and are inconsistent • Parallel lines have the same slope but different y-intercepts • Lines with the same slopes and the same y-intercepts are consistent • Lines with different slopes, regardless of the y-intercept intersect with 1 solution

  10. The Rules • Different slopes • 1 solution • Same Slopes, Different Y-Intercept • No Solutions, Inconsistent • Same Slopes, Same Y-Intercept • Infinitely Many Solutions, Consistent

  11. Example • Without solving the linear system, tell whether the linear system has one solution, no solution or infinitely many solutions.

  12. Homework • 7.5 • 2-14 even, 24-32 even, 36, 39

  13. Practical Practice • A pizza parlor fills two pizza orders. Find the cost of one medium pizza

  14. Most Important Points • Systems of equations sometimes have no solutions or infinitely many solutions • Definition of an inconsistent and consistent system • Rules for knowing the number of solutions

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