document.write( "Question 538708: Can you please help me discern how to graph a solution for the two lines: 1/2x-y=3 and x=6+2y \n" ); document.write( "

Algebra.Com's Answer #353245 by KMST(5328) $\"\"$ $\"About$

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$\"%281%2F2%29x-y=3\"$ and $\"x=6%2B2y\"$ ?
\n" ); document.write( "Those are the equations of straight lines. Two points determine a line, so you just need 2 point for each line.
\n" ); document.write( "Sometimes making x=0 to solve for y gives you a useful point.
\n" ); document.write( "Sometimes making y=0 to solve for x gives you a useful point.
\n" ); document.write( "Sometimes you can get two useful points doing that.
\n" ); document.write( "I assume you are graphing the lines to solve the system of equations.
\n" ); document.write( "For $\"%281%2F2%29x-y=3\"$
\n" ); document.write( "x=0---> $\"-y=3\"$ ---> $\"y=-3\"$ gives you point (0, -3).
\n" ); document.write( "y=0---> $\"%281%2F2%29x=3\"$ ---> $\"x=6\"$ gives you point (6, 0).
\n" ); document.write( "Those are good points, easy to plot and far apart enough to let you draw the line accurately.
\n" ); document.write( "For $\"x=6%2B2y\"$
\n" ); document.write( "x=0---> $\"0=6%2B2y\"$ ---> $\"2y=-6\"$ ---> $\"y=-3\"$ gives you point (0, -3).
\n" ); document.write( "y=0---> $\"x=6\"$ gives you point (6, 0).
\n" ); document.write( "Those are good points, easy to plot and far apart enough to let you draw the line accurately.
\n" ); document.write( "Surprise! It's the same line. We even picked the same two points.
\n" ); document.write( "The solution to the system of equations is all the infinite points in that line.
\n" ); document.write( "The equations are dependent.
\n" ); document.write( "If your lines were parallel, it would be an inconsistent system with no solutions.
\n" ); document.write( "If the lines intersected, the intersection point would be your solution. \n" ); document.write( "

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