document.write( "Question 103098: Solve each of the following systems by graphing. help please.\r
\n" ); document.write( "\n" ); document.write( "2x - y = 4
\n" ); document.write( "2x - y = 6 \n" ); document.write( "
Algebra.Com's Answer #74988 by doukungfoo(195)\"\" \"About 
You can put this solution on YOUR website!
What does it mean to solve a system of equations by graphing?
\n" ); document.write( "What you are being asked to do is graph each equation and then note the point at which they intersect. This intersection is the solution for the system.
\n" ); document.write( "To begin with write each equation in slope intercept form.
\n" ); document.write( "Slope intercept form is:
\n" ); document.write( "y = mx + b
\n" ); document.write( "m is the slope of the line
\n" ); document.write( "and b is the y intercept (the point at which the line crosses the y axis)
\n" ); document.write( "So lets look at the first equation
\n" ); document.write( "2x - y = 4
\n" ); document.write( "move 2x to the right side of the equation
\n" ); document.write( "to do this subtract 2x from both sides
\n" ); document.write( "2x - 2x - y = -2x + 4
\n" ); document.write( "-y = -2x + 4
\n" ); document.write( "next get rid of the negative sign in front of the y
\n" ); document.write( "to do this divide both sides by -1
\n" ); document.write( "-y/-1 = -2x/-1 + 4/-1
\n" ); document.write( "y = 2x - 4
\n" ); document.write( "Ok now we have this equation in slope intercept form
\n" ); document.write( "the slope is 2
\n" ); document.write( "and the y intercept is -4
\n" ); document.write( "Lets graph the line
\n" ); document.write( "start at the y intercept -4
\n" ); document.write( "Place a dot on your graph at point (0,-4)
\n" ); document.write( "Now slope is defined as \"rise%2Frun\"
\n" ); document.write( "since the slope for this line is 2 which is equal to \"2%2F1\"
\n" ); document.write( "the rise is 2 and the run is 1
\n" ); document.write( "Starting at the y intercept point (0,-4) we are going to use the slope to
\n" ); document.write( "find the next point on this line
\n" ); document.write( "So place your pencil at point (0,-4) on the graph
\n" ); document.write( "now rise up 2
\n" ); document.write( "your pencil should be at point (0,-2) on the graph
\n" ); document.write( "now run to the right 1
\n" ); document.write( "Now your pencil should be at point (1,-2) mark a dot here
\n" ); document.write( "Ok now use a ruler to draw a line through both points
\n" ); document.write( "Your graph should now look like this:
\n" ); document.write( "\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+2x-4%29+\"
\n" ); document.write( "Ok now follow these same steps to graph the second equation
\n" ); document.write( "2x - y = 6
\n" ); document.write( "2x - 2x - y = -2x + 6
\n" ); document.write( "-y = -2x + 6
\n" ); document.write( "-y/-1 = -2x/-1 + 6/-1
\n" ); document.write( "y = 2x - 6
\n" ); document.write( "slope for this line is 2 or \"2%2F1\"
\n" ); document.write( "y intercept is -6
\n" ); document.write( "Graph it following the same steps as before
\n" ); document.write( "only this time the starting point is (0,-6) because that is the y intercept for this line
\n" ); document.write( "Now the graph contains both lines:
\n" ); document.write( "\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+2x-4%2C+2x-6%29+\"
\n" ); document.write( "So looking at the graph we can see that the lines are parallel.
\n" ); document.write( "There is no point of intersection.
\n" ); document.write( "This means there are no solutions, and the system is called inconsistent. \r
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