document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=68733>Question 68733</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1:  Plot the graph of the equation 2x-3y=6 and 2x+y=-10 and intercept the result.<BR>\n" );
document.write( "2:  Plot the graph of the equations 2x+4y=10 and 3x+6y=12 and intercept the result.<BR>\n" );
document.write( "3:  Determine graphically the vertices of the triangle, the equation of whose sides are given y=x; y=0; 2x+3y=10, interpret the result? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #48941 by </B><A HREF=/tutors/aboutme.mpl?userid=rmromero><B>rmromero(383)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rmromero><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=48941\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1: Plot the graph of the equation 2x-3y=6 and 2x+y=-10 and intercept the result.<BR>\n" );
document.write( "<br> To graph the equations, rewrite the equations written in standard form to slope-intercept form of the equation. y = mx + b <BR>\n" );
document.write( "2x-3y=6<BR>\n" );
document.write( "3y = 2x + 6<BR>\n" );
document.write( "y = 2/3x + 2\r<BR>\n" );
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document.write( "<br><BR>\n" );
document.write( "2x+y=-10 <BR>\n" );
document.write( "y = -2x - 10\r<BR>\n" );
document.write( "\n" );
document.write( "<br> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28200%2C+200%2C+-7%2C+4%2C+-8%2C+6%2C+%282%2F3%29x-2%2C+%28-2%29x-10%29 ALIGN=MIDDLE  ALT=\"graph+%28200%2C+200%2C+-7%2C+4%2C+-8%2C+6%2C+%282%2F3%29x-2%2C+%28-2%29x-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<br> To solve for the intercept, We will use substitution method.<BR>\n" );
document.write( "1. In either equation, solve for one variable in terms of the other.<BR>\n" );
document.write( "2x+y=-10 <BR>\n" );
document.write( "y = -2x - 10<BR>\n" );
document.write( "<br><BR>\n" );
document.write( "2. Substitute for that variable in the other equation. Solve.<BR>\n" );
document.write( "2x-3y=6<BR>\n" );
document.write( "2x - 3(-2x-10) = 6<BR>\n" );
document.write( "2x + 6x + 30 = 6<BR>\n" );
document.write( "8x + 30 = 6<BR>\n" );
document.write( "8x = -24<BR>\n" );
document.write( "x = -3<BR>\n" );
document.write( "3. Substitute the result from step 2 in either equation. Solve for the other variable.<BR>\n" );
document.write( "2x+y=-10 , x = -3<BR>\n" );
document.write( "2(-3)+y = -10<BR>\n" );
document.write( "-6 + y = -10<BR>\n" );
document.write( "y = -4<BR>\n" );
document.write( "4. Check the solution in both original equations.<BR>\n" );
document.write( "2x+y=-10, x = -3, y = -4<BR>\n" );
document.write( "2(-3) + (-4) = -10<BR>\n" );
document.write( "-6 -4 = -10<BR>\n" );
document.write( "-10 = -10 --------->> True<BR>\n" );
document.write( "<br><BR>\n" );
document.write( "2x-3y=6, x = -3, y = -4<BR>\n" );
document.write( "2(-3)-3(-4) = 6<BR>\n" );
document.write( "-6 + 12 = 6<BR>\n" );
document.write( "6 = 6 ---------->> True<BR>\n" );
document.write( "<br> Therefore the lines intersect when x = -3 and y = -4 \r<BR>\n" );
document.write( "\n" );
document.write( "<br><br><BR>\n" );
document.write( "2: Plot the graph of the equations 2x+4y=10 and 3x+6y=12 and intercept the result.<BR>\n" );
document.write( "<br> To graph the equations, rewrite the equations written in standard form to slope-intercept form of the equation. y = mx + b <BR>\n" );
document.write( "2x+4y=10 <BR>\n" );
document.write( "4y = -2x+10<BR>\n" );
document.write( "y = (-2/4)x+10/4<BR>\n" );
document.write( "y = (-1/2)x+(5/2) <BR>\n" );
document.write( "<br><BR>\n" );
document.write( "3x+6y=12 <BR>\n" );
document.write( "6y = -3x+12<BR>\n" );
document.write( "y = (-3/6)x+(12/6)<BR>\n" );
document.write( "y = (-1/2)x+2\r<BR>\n" );
document.write( "\n" );
document.write( "<br> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28200%2C+200%2C+-4%2C+4%2C+-2%2C+4%2C+%28-1%2F2%29x%2B%285%2F2%29%2C+%28-1%2F2%29x%2B2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<br> To solve for the intercept, We will use substitution method.<BR>\n" );
document.write( "1. In either equation, solve for one variable in terms of the other.<BR>\n" );
document.write( "3x+6y=12 <BR>\n" );
document.write( "6y = -3x+12<BR>\n" );
document.write( "y = (-3/6)x+(12/6)<BR>\n" );
document.write( "y = (-1/2)x+2<BR>\n" );
document.write( "<br><BR>\n" );
document.write( "2. Substitute for that variable in the other equation. Solve.<BR>\n" );
document.write( "2x+4y=10 <BR>\n" );
document.write( "2x + 4((-1/2)x+2) = 10<BR>\n" );
document.write( "2x + -2x + 8 = 10<BR>\n" );
document.write( "8 = 10 ---------->> Not True\r<BR>\n" );
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document.write( "<br> Therefore the lines do not have an intersection. <BR>\n" );
document.write( " <BR>\n" );
document.write( "3: Determine graphically the vertices of the triangle, the equation of whose sides are given y=x; y=0; 2x+3y=10, interpret the result?\r<BR>\n" );
document.write( "\n" );
document.write( "<br> Graph each equation y=0. Since y=x, then x=0. <BR>\n" );
document.write( "To graph 2x+3y =10, we are going find y-intercept and x-intercept<BR>\n" );
document.write( "2x+3y=10<BR>\n" );
document.write( "To find y-intercept by substituting 0 for x.<BR>\n" );
document.write( "2(0) + 3y = 10<BR>\n" );
document.write( "3y = 10<BR>\n" );
document.write( "y = 10/3 ----->y-intercept (0, 10/3)\r<BR>\n" );
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document.write( "<br><BR>\n" );
document.write( "To find x-intercept by substituting 0 for y.<BR>\n" );
document.write( "2x + 3(0) = 10<BR>\n" );
document.write( "2x = 10<BR>\n" );
document.write( "x = 5 --------->> x-intercept (5, 0)\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28200%2C+200%2C+-2%2C+7%2C+-2%2C+7%2C+%28-2%2F3%29x%2B%2810%2F3%29%2C+y=0%2C+x=0%29 ALIGN=MIDDLE  ALT=\"graph+%28200%2C+200%2C+-2%2C+7%2C+-2%2C+7%2C+%28-2%2F3%29x%2B%2810%2F3%29%2C+y=0%2C+x=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice that the y-intercept (0, 10/3) is one of the vertex of the triangle. x-intercept (5, 0) is the other vertex of the triangle formed. And lastly, the origin (0,0).<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );