1. Essential Question: What does the graph of an independent system of linear equations in two variables look like?

2.  Get both lines into slope-intercept form  y = mx + b  Get “y” by itself  Graph each line  Plot y-intercept (“b”) on the y-axis  Use the slope (“m” – rise over run) to make a second point  Connect the two points  Solution is where the two lines intersect

3.  Solve by graphing  2x + y = 5  -x + y = 2  Solve both equations for y   Graph both lines on the same grid  Intersection is the solution y = -2x + 5 y = x + 2 solution: (1, 3)

4.  What does that point (1, 3) mean?  It means that x = 1 and y = 3 is a solution to both equations. ▪ 2x + y = 5 2(1) + (3) = 5 2 + 3 = 5 ▪ -x + y = 2 -(1) + (3) = 2 -1 + 3 = 2

5.  Independent System – 1 solution  Intersecting Lines  Lines have different slopes  Inconsistent System – No solution  Parallel Lines  Lines have same slope & different y-intercepts  Dependent System – Infinite solutions  Same line  Lines have same slope & same y-intercept

6.  Classify the system without graphing  y = 2x + 3-2x + y = 1  Solve both equations for y   Do the graphs have the same slope?  Yes? See next questionNo? Independent  Are they the same line? ▪ Yes? DependentNo? Inconsistent y = 2x + 3 y = 2x + 1

7.  Classify the system without graphing  y = 2x + 3-4x + 2y = 6  Solve both equations for y   Do the graphs have the same slope?  Yes? See next questionNo? Independent  Are they the same line? ▪ Yes? DependentNo? Inconsistent y = 2x + 3 y = 2x + 3

8.  Assignment  Page 120 – 121  1 – 7 & 13 – 23, odd problems  Show work (e.g. converting equations)