document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=177760>Question 177760</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Linear System<BR>\n" );
document.write( "Solve by elimination. Check each solution.<BR>\n" );
document.write( "a) 2a+b=5<BR>\n" );
document.write( "   a-2b=10\r<BR>\n" );
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document.write( "b) 4k+3h=12<BR>\n" );
document.write( "   4k-h=4<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #132770 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=132770\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <FONT FACE=\"Times New Roman\" SIZE=\"4\">I'll do the first one of these and you can repeat the process for the other one.\r<BR>\n" );
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document.write( "Equation 1: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \text {  } \math 2a + b = 5\"><BR>\n" );
document.write( "Equation 2: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \text {  } \math a - 2b = 10\">\r<BR>\n" );
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document.write( "Step 1:  Multiply Eq. 1 by 2 so that the coefficients on the b terms are additive inverses (one is already -2 and the other becomes 2):\r<BR>\n" );
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document.write( "Equation 3: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \text {  } \math 4a + 2b = 10\">\r<BR>\n" );
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document.write( "Step 2:  Add Eq 3 to Eq 2, term by term, eliminating the b variable (hence the name of the method)\r<BR>\n" );
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document.write( "Equation 4: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \text {  } \math 4a + a + 2b - 2b = 10 + 10 \text{ } \Rightarrow \text{ } \math 5a = 20 \text{ } \Rightarrow \text{ } \math a = 4\">\r<BR>\n" );
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document.write( "Step 3:  Substitute the value determined for a into either of the original equations and then solve for b:\r<BR>\n" );
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document.write( "Equation 2: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \text {  } \math 4 - 2b = 10\text{ } \Rightarrow \text{ } \math -2b = 6 \text{ } \Rightarrow \text{ } \math b = -3\">\r<BR>\n" );
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document.write( "Hence, the solution set for the system:\r<BR>\n" );
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document.write( "Equation 1: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \text {  } \math 2a + b = 5\"><BR>\n" );
document.write( "Equation 2: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \text {  } \math a - 2b = 10\">\r<BR>\n" );
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document.write( "is the ordered pair <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (a, b) = (4, -3)\">\r<BR>\n" );
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document.write( "Checking the answer is left as an exercise for the student.<BR>\n" );
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