document.write( "Question 103229: Solve each of the following systems by graphing.\r
\n" ); document.write( "\n" ); document.write( "x-2y=8\r
\n" ); document.write( "\n" ); document.write( "3x-2y=12 \n" ); document.write( "
Algebra.Com's Answer #75085 by doukungfoo(195)\"\" \"About 
You can put this solution on YOUR website!
First we need to put 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 and
\n" ); document.write( "b is y intercept
\n" ); document.write( "Ok so the first equation is:
\n" ); document.write( "x - 2y = 8
\n" ); document.write( "first go ahead a place a 1 in front of the x
\n" ); document.write( "this is just a good way to remember that it is there (x=1*x=1x)
\n" ); document.write( "1x - 2y = 8
\n" ); document.write( "now move the 1x over by subtracting it from both sides
\n" ); document.write( "1x - 1x - 2y = -1x + 8
\n" ); document.write( "the 1x's on the right side cancel out leaving
\n" ); document.write( "-2y = -1x + 8
\n" ); document.write( "now divide both sides by -2
\n" ); document.write( "-2y/-2 = -1x/-2 + 8/-2
\n" ); document.write( "\"y+=+%281%2F2%29x+-+4\"
\n" ); document.write( "now we have the equation in slope intercept form y = mx + b
\n" ); document.write( "and we can easily see that
\n" ); document.write( "slope is \"1%2F2\"
\n" ); document.write( "and the y intercept is -4
\n" ); document.write( "Now we are ready to graph this line
\n" ); document.write( "Start at the y intercept
\n" ); document.write( "The y intercept is where the line crosses the y axis so this is a known point on the line we are trying to graph.
\n" ); document.write( "Since we know that the y intercept for this line is -4
\n" ); document.write( "move your pencil to point (0,-4) and mark a dot on the graph
\n" ); document.write( "Now lets look at the slope
\n" ); document.write( "slope is defined as \"rise%2Frun\"
\n" ); document.write( "The slope for this line is \"1%2F2\"
\n" ); document.write( "so we are going to rise up 1 and run to the right 2
\n" ); document.write( "Place your pencil over the dot we just marked at point (0,-4)
\n" ); document.write( "and rise up 1
\n" ); document.write( "you should be at point (0,-3) on the graph
\n" ); document.write( "now run to the right 2
\n" ); document.write( "you should be at point (2,-3) on the graph
\n" ); document.write( "mark a dot here.
\n" ); document.write( "Now using a ruler line up the dots and draw a line through them.
\n" ); document.write( "Here is what your graph should look like.\r
\n" ); document.write( "\n" ); document.write( "\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+%28x%2F2%29-4%29+\"
\n" ); document.write( "Now lets graph the second equation
\n" ); document.write( "3x - 2y = 12
\n" ); document.write( "Follow the same steps as we did for the first equation
\n" ); document.write( "first put the equation in slope intercept form
\n" ); document.write( "3x - 2y = 12
\n" ); document.write( "3x - 3x - 2y = -3x + 12
\n" ); document.write( "-2y = -3x + 12
\n" ); document.write( "-2y/-2 = -3x/-2 + 12/-2
\n" ); document.write( "\"y+=+%283%2F2%29x-6\"
\n" ); document.write( "Ok so the slope for this line is \"3%2F2\"
\n" ); document.write( "and the y intercept is -6
\n" ); document.write( "Lets graph it.
\n" ); document.write( "Again use the same steps as we did for the first line
\n" ); document.write( "start at the y intercept for this line
\n" ); document.write( "mark a dot at point (0,-6)
\n" ); document.write( "and the slope for this line is \"3%2F2\"
\n" ); document.write( "so from point (0,-6)
\n" ); document.write( "rise up 3
\n" ); document.write( "and run to the right 2
\n" ); document.write( "you should be at point (2,-3) on the graph
\n" ); document.write( "using a ruler draw a line through both points
\n" ); document.write( "now your graph should look like this.
\n" ); document.write( "\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+%28x%2F2%29-4%2C+%283x%2F2%29-6%29+\"
\n" ); document.write( "The point at which the lines intersect is the solution for this system of equations.
\n" ); document.write( "the point of intersection is (2,-3)
\n" ); document.write( "This means that for this system of equations x = 2 and y = -3
\n" ); document.write( "Lets check these solutions in the original equations
\n" ); document.write( "first equation:
\n" ); document.write( "x - 2y = 8
\n" ); document.write( "substitute x with 2 and y with -3
\n" ); document.write( "2 - 2(-3) = 8
\n" ); document.write( "2 + 6 = 8
\n" ); document.write( "8 = 8
\n" ); document.write( "Ok now try the second equation
\n" ); document.write( "3x - 2y = 12
\n" ); document.write( "3(2) - 2(-3) = 12
\n" ); document.write( "6 + 6 = 12
\n" ); document.write( "12 = 12
\n" ); document.write( "Our solution satisfies both equations so we can be sure we have found the correct solution for this system of equations. \n" ); document.write( "
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