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Chapter 12—Graphing

12-5 Solving Systems of Linear Equations

Some very interesting things happen when you plot two different  linear equations on the same coordinate plane. The main thing is this:  As long as the two lines do not have the same slope, they intersect (or cross) at some point.

[show one line, two lines and point of intersection]

[if lines have the same slope, they will not  cross because they are parallel]

 Graphically solve this system of linear equations y = 2x + 1 y = -x + 4 Determine the x- and y-intercepts for the first equation and sketch line L1: when x = 0 y = 1 when y = 0, x = - 1/2 Plot those two intercepts-- (0,1) and (0, -1/2) Draw the straight line, L1, through those two points Determine the x- and y-intercepts for the second equation and sketch line L2: when x = 0,  y = 4 when y = 0, x = 4 Plot those two intercepts-- (0,4) and (4, 0) Draw the straight line, L2, through those two points   The solution for the system of linear equations is the point where the two lines intersect: (1,4) y = 2x + 1 and y = -x + 4 only when x = 1 and y = 4 Examples & Exercises

 Given the slope and one point on a line, write the linear equation for the line in slope-intercept form.

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