document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=170899>Question 170899</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Equations with two variables:\r<BR>\n" );
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document.write( "Solve for x and y:<BR>\n" );
document.write( "8x + 2y = 7<BR>\n" );
document.write( "3x - 4y = 5\r<BR>\n" );
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document.write( "Could you please, give me the answer by parts?  I will appreciate if you give me the answer, and understand the questions by parts, because I need to learn who to resolve this type equations?\r<BR>\n" );
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document.write( "thank you for your help. jessica </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #126173 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=126173\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve for x and y:<BR>\n" );
document.write( "8x + 2y = 7<BR>\n" );
document.write( "3x - 4y = 5 <BR>\n" );
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document.write( "There are two ways to solve these, elimination and substitution. <BR>\n" );
document.write( "Elimination:<BR>\n" );
document.write( "You multiply one or both equations so when the equations are added or subtracted, one of the variables is eliminated. Then it is easy to solve for the other variable:<BR>\n" );
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document.write( "Multiply the 1st equation by 2 and you have:<BR>\n" );
document.write( "16x + 4y = 14<BR>\n" );
document.write( " 3x - 4y = 5<BR>\n" );
document.write( "----------------Adding will eliminate y:<BR>\n" );
document.write( "19x + 0y = 19<BR>\n" );
document.write( "or<BR>\n" );
document.write( "19x = 19<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19%2F19 ALIGN=MIDDLE  ALT=\"19%2F19\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 1<BR>\n" );
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document.write( "Now substitute 1 for x in one of the original equations, we'll use the 1st one.<BR>\n" );
document.write( "8(1) + 2y = 7<BR>\n" );
document.write( "8 + 2y = 7<BR>\n" );
document.write( "2y = 7 - 8; subtracted 8 from both sides<BR>\n" );
document.write( "2y = -1<BR>\n" );
document.write( "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;\" ><BR>\n" );
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document.write( "Check solutions by substituting both solutions in the 2nd original equation.<BR>\n" );
document.write( "3(1) - 4(-1/2) = 5<BR>\n" );
document.write( "3 + 2 = 5; remember minus a minus is a plus<BR>\n" );
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document.write( "Did this help you understand these problems? </SPAN>\n" );
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