Lesson 7.5 Solve Special Types of Linear Systems

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Presentation transcript:

Lesson 7.5 Solve Special Types of Linear Systems Essential Question: How can you identify the number of solutions of a linear system?

Before we start… Graph 𝑦=− 1 2 𝑥+2 and 𝑦=− 1 2 𝑥−3 in the same coordinate plane. What do you notice about these lines?

Classifying Systems CONSISTENT INCONSISTENT -A system that has at least one solution *INDEPENDENT Exactly one solution *DEPENDENT Infinitely many solutions INCONSISTENT -A system that has no solution

How do you identify the number of solutions ? The slope and y-intercept can tell you the number of solutions. Number of Solutions Slopes and y-intercepts One solution Different slopes No solution Same slope Different y-intercepts Infinitely many solutions Same y-intercept

Graph the system. Tell how many solutions the system has.

Graph the system. Tell how many solutions the system has.

Graph the system. Tell how many solutions the system has.

Graph the system. Tell how many solutions the system has.

Graph the system. Tell how many solutions the system has.

Graph the system. Tell how many solutions the system has.

Solve the linear system algebraically.

Solve the linear system algebraically.

Solve the linear system algebraically.

Solve the linear system algebraically.

Solve the linear system algebraically.

Solve the linear system algebraically.

How can you identify the number of solutions of a linear system?

Ticket Out the Door How many solutions does this system have?