7.1 (b) Systems of Linear Equations - Solve by Graphing - Post 1

Looking at the Cartesian plane above you will see two distinct linear equations.  The equations are in standard form rather than slope-intercept form.  I've mentioned that we will be using standard form more as we progress through chapter 7.  Doesn't mean we have to like it (I don't) for graphing equations:)

So as you look at these two functions (equations) graphed above, you should notice that the lines represent a solution set (list of answers) for each linear equation.  I can prove this to you by plugging in and solving for one of the points:

• Looking at the blue line (4x-6y=12), I see it crosses the y-axis at (0,-2).  I will put the coordinates (x,7) for this point into the equation to show it is a correct solution to the function:
• 4x   -   6y     = 12
• 4(0) -  6(-2) = 12 (note that -6 times -2 equals +12)
• 0      +  12   = 12 
•             12   = 12  
• You can see that 12 does in fact equal 12 so this is a correct solution for this function.

Go ahead and prove that the coordinate (3,0), where the two lines intersect, is a solution for both linear equations by plugging that into both functions.