Topic: Solving Systems of Linear Equations by Graphing

What is a system of equations? Set of equations with two or more variables. Example: x + 2y = 6 x – y = 3 Solution to a system of linear equations is an ordered pair that makes each equation true. Example: (4, 1) is the solution to the above system, because it makes each equation true (1) = 6 4 – 1 = 3

Types of systems (Put on a note card) Independent system System with exactly one solution. Graph of system contains two intersecting lines (equations have different slopes). Dependent system System with infinitely many solutions. Graph of system contains coinciding lines (both equations have same slope & y-intercept). Inconsistent system System with no solutions. Graph of system contains parallel lines (same slope, different y-intercepts).

Solving Linear Systems: Graphing Graph each equation. The point where the two lines intersect is the solution to the system. You should ALWAYS check your solution algebraically by substituting the solution point for x & y in each equation.

Graph each line and find the intersection. The lines appear to intersect at (2, 1). Check solution algebraically by substituting (2, 1) into each equation. { Solving Linear Systems: Graphing

Both statements are true; (2, 1) is the solution to this system. { Solving Linear Systems: Graphing

This second equation is ugly! Let’s rewrite in slope-intercept form. Move y to the left and x to the right. { Solving Linear Systems: Graphing Both lines have the same slope, so they are parallel. This is an inconsistent system with no solution (so there’s no reason for us to actually graph it).

JOURNAL ENTRY TITLE: Solving Systems Graphically Review your notes from this presentation and identify 3 things you already knew, 2 things you learned, and one question you still have.

Homework Textbook Section 6-1 (pg. 386): 2-16 Due 1/17 (B-day) or 1/18 (A-day)