document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=664285>Question 664285</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A triangle is formed by the intersection of the lines 2x + 3y = 14<BR>\n" );
document.write( "4X - 5y= - 16 and the x- axis.Find the area of the triangle<BR>\n" );
document.write( "Thank you so much . </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #413216 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=413216\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2x+3y=14<BR>\n" );
document.write( "as a linear equation<BR>\n" );
document.write( "3y =-2x+14<BR>\n" );
document.write( "y = -2/3x+14/3<BR>\n" );
document.write( "and <BR>\n" );
document.write( "4x-5y =-16<BR>\n" );
document.write( "as a linear equation<BR>\n" );
document.write( "5y = 4x+16<BR>\n" );
document.write( "y = 4/5x + 16/5<BR>\n" );
document.write( "...<BR>\n" );
document.write( "y = -2/3x+14/3<BR>\n" );
document.write( "y = 4/5x + 16/5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-10%2C10%2C-1%2C5%2C%28-2%2F3%29x%2B%2814%2F3%29%2C%284%2F5%29x%2B%2816%2F5%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "...<BR>\n" );
document.write( "Graphically, we see the base of the triangle is from -4 and 7.  The height of the triangle is 4.  Area = 1/2bh = 1/2(11*4) = 22<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Numerically,<BR>\n" );
document.write( "To find the base you find the point where each line crosses the x axis and calculate the difference between those points.<BR>\n" );
document.write( "y=-2/3x +14/3 crosses the x axis when y=0<BR>\n" );
document.write( "0=-2/3x +14/3<BR>\n" );
document.write( "2/3x=14/3<BR>\n" );
document.write( "2/3x(3/2)=14/3(3/2)<BR>\n" );
document.write( "x=7<BR>\n" );
document.write( "The right bottom corner is at (7,0)<BR>\n" );
document.write( "...<BR>\n" );
document.write( "y=4/5x + 16/5<BR>\n" );
document.write( "0=4/5x + 16/5<BR>\n" );
document.write( "-4/5x = 16/5<BR>\n" );
document.write( "-4/5x(5/4) = 16/5(-5/4)<BR>\n" );
document.write( "x=-4<BR>\n" );
document.write( "The left bottom corner is at (-4,0)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "The distance between -4 and 0 is |-4| which is the same as 4 and the distance between 0 and 7 is |7| which is the same as 7.  The distance between the x intercept points is 7+4=11.  This is the base.<BR>\n" );
document.write( "Alternatively, the difference in points is (7) -(-4)=11<BR>\n" );
document.write( "...<BR>\n" );
document.write( "The place where the line intersect is found by setting the two linear equations  equal, as they share the y intersect point.<BR>\n" );
document.write( "4/5x + 16/5 = -2/3x + 14/3<BR>\n" );
document.write( "Isolate x<BR>\n" );
document.write( "4/5x + 2/3x = 14/3 - 16/5<BR>\n" );
document.write( "Multiply the entire expression by 15<BR>\n" );
document.write( "12x + 10x = 70 - 48<BR>\n" );
document.write( "22x = 22<BR>\n" );
document.write( "x=1<BR>\n" );
document.write( "The lines intersect where x = 1<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Plug the x intersect of 1 back into the equation to find the y value at that intersection<BR>\n" );
document.write( "y = -2/3(1) + 14/3 = 12/3 = 4<BR>\n" );
document.write( "Double check with the other equation<BR>\n" );
document.write( "y = 4/5(1) + 16/5 = 20/5 = 4<BR>\n" );
document.write( "Both lines have a y point of 4 when x is 1<BR>\n" );
document.write( "Therefore, they intersect at (1,4)<BR>\n" );
document.write( "The y value indicates the height of the created triagle as 4<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Area = 1/2bh<BR>\n" );
document.write( "b=11<BR>\n" );
document.write( "h=4<BR>\n" );
document.write( "a = 1/2(11*4) = 1/2(44)= 22<BR>\n" );
document.write( ".........................<BR>\n" );
document.write( "Delighted to help.<BR>\n" );
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