Solve the linear system. 1. x – 2y = 5 2. 3x + 7y = -29 x + 3y = -10 4x + 3y = -7 3. Santa went on a shopping spree. At his first stop he spent $7200 and.

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Presentation transcript:

Solve the linear system. 1. x – 2y = x + 7y = -29 x + 3y = -10 4x + 3y = Santa went on a shopping spree. At his first stop he spent $7200 and bought 300 toys (same type) and 1200 rolls of wrapping paper. On his next stop he spent $25,260 and bought 600 toys and 6020 rolls of wrapping paper. How much was the wrapping paper? (-1, -3) (2, -5) 300t w = t w = The wrapping paper Santa bought was $3 each.

DQ TIME Pencil and calculator only Show all of your work on the daily quiz Make sure your name is on your paper Turn it in on the rolling cart when you are finished.

So far we have had one solution for each of our systems. Some linear systems can have no solution or infinitely many solutions. Today we are going to find out how to determine how many solutions a system has and why.

Exactly one solution y x

Infinitely many solutions y x

NO solution y x

Same number equals same number…. many solutions. A number equals a different number…. no solutions.

A) Solve using any method. B) Tell how many solutions the system has. C) Explain why the system has the indicated number of solutions. Ex: 1 Number of solutions: Explain why: Solve:

A) Solve using any method. B) Tell how many solutions the system has. C) Explain why the system has the indicated number of solutions. Ex: 2 Number of solutions: Explain why: Solve:

A) Solve using any method. B) Tell how many solutions the system has. C) Explain why the system has the indicated number of solutions. Ex: 3 Number of solutions: Explain why: Solve:

A) Solve using any method. B) Tell how many solutions the system has. C) Explain why the system has the indicated number of solutions. Ex: 4 Number of solutions: Explain why: Solve:

A) Solve using any method. B) Tell how many solutions the system has. C) Explain why the system has the indicated number of solutions. Ex: 5 Number of solutions: Explain why: Solve:

Solve the linear system and tell how many solutions the system has and explain why. 1.x + y = 3 2x + 2y = 4 2. x + y = 3 2x + 2y = 6 3. x + y = 3 x + 2y = 4 1.No solutions because lines are parallel 2. Many Solutions because lines coincide 3.(2, 1); One solution because lines intersect