document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=692098>Question 692098</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph the system of equations. Then determine whether the system has \"no solution\" , \"one solution\", or \"infinite solutions\". If the system ha one solution name it.<BR>\n" );
document.write( "Y= -1/2x + 3<BR>\n" );
document.write( "Y= 2x - 2<BR>\n" );
document.write( "(it shows just a plain graph) <BR>\n" );
document.write( "I know it's \"y= m(x) + b\" but idk if I should use m = y2 - y1 over x2 - x1 I'm really confused. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #426927 by </B><A HREF=/tutors/aboutme.mpl?userid=ReadingBoosters><B>ReadingBoosters(3246)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ReadingBoosters><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=426927\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are given the equation for both lines in the slope-intercept form(y=mx+b).<BR>\n" );
document.write( "...<BR>\n" );
document.write( "You can determine the solution to the system of equations algebraically and graphically.<BR>\n" );
document.write( "...<BR>\n" );
document.write( "To solve it graphically, you will graph each line and the solution is where the lines intersect.<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Just by looking at the equations, you can tell that not only will they intersect, but the lines are perpendicular.  <BR>\n" );
document.write( "Perpendicular lines have negative inverse/reciprocal slope.<BR>\n" );
document.write( "In the first line y=-1/2x + 3, the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "In the second line y= 2x - 2, the slope is 2.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the negative reciprocal of 2<BR>\n" );
document.write( "...<BR>\n" );
document.write( "To graph a line, find the x and y intercept and draw a line through them.<BR>\n" );
document.write( "the y intercept is b in the y=mx+b format<BR>\n" );
document.write( "the x intercept is x when y is 0<BR>\n" );
document.write( "...<BR>\n" );
document.write( "For y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >x+3<BR>\n" );
document.write( "y intercept is 3, so plot (0, 3)<BR>\n" );
document.write( "x intercept is found by:<BR>\n" );
document.write( "0 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 3<BR>\n" );
document.write( "-3 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >x<BR>\n" );
document.write( "-3(-2) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2F2%29%28-2%29x ALIGN=MIDDLE  ALT=\"%28-1%2F2%29%28-2%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "6 = x, so plot (6, 0)<BR>\n" );
document.write( "Then draw a line through the intercepts, so that it looks like:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28200%2C100%2C-10%2C10%2C-10%2C10%2C%28-1%2F2%29x%2B3%29 ALIGN=MIDDLE  ALT=\"graph%28200%2C100%2C-10%2C10%2C-10%2C10%2C%28-1%2F2%29x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "...<BR>\n" );
document.write( "For y = 2x - 2<BR>\n" );
document.write( "y intercept is -2, so plot (0, -2)<BR>\n" );
document.write( "x intercept is found by <BR>\n" );
document.write( "01 = 2x - 2<BR>\n" );
document.write( "2 = 2x<BR>\n" );
document.write( "1 = x, so plot (1, 0)<BR>\n" );
document.write( "Then draw a line through the intercepts and your graph should look like:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C%28-1%2F2%29x%2B3%2C2x-2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C%28-1%2F2%29x%2B3%2C2x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "...<BR>\n" );
document.write( "The \"one solution\" to the system is the point where they intercept,<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%282%29 ALIGN=MIDDLE  ALT=\"highlight_green%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%282%29 ALIGN=MIDDLE  ALT=\"highlight_green%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "....<BR>\n" );
document.write( "Algebraically, set the two equations equal to each other and solve for x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2F2%29x%2B3+=+2x-2 ALIGN=MIDDLE  ALT=\"%28-1%2F2%29x%2B3+=+2x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ==> multiply both sides by 2<BR>\n" );
document.write( "-1x + 6 = 4x - 4<BR>\n" );
document.write( "6 + 4 = 4x + x<BR>\n" );
document.write( "10 = 5x<BR>\n" );
document.write( "x=2<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Plug in x into either equation and solve for y<BR>\n" );
document.write( "y = 2(2) - 2 = 4-2<BR>\n" );
document.write( "y = 2<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Confirmed, the solution/point of intersection is (2,2)<BR>\n" );
document.write( "………………………<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );