document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197249>Question 1197249</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve by using elimination method\r<BR>\n" );
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document.write( "8x+4y=16<BR>\n" );
document.write( "4x-7y=26<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 #830445 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=830445\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "4x-7y=26 is equivalent to 8x-14y=52 after multiplying both sides by 2.\r<BR>\n" );
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document.write( "We have this equivalent system of equations<BR>\n" );
document.write( "8x+4y=16<BR>\n" );
document.write( "8x-14y=52\r<BR>\n" );
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document.write( "Subtract the equations straight down.<BR>\n" );
document.write( "8x-8x becomes 0<BR>\n" );
document.write( "4y-(-14y) becomes 18y<BR>\n" );
document.write( "16-52 becomes -36\r<BR>\n" );
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document.write( "We're left with 18y = -36 which solves to y = -2<BR>\n" );
document.write( "I divided both sides by 18 to isolate y.\r<BR>\n" );
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document.write( "Use this y value to find x.<BR>\n" );
document.write( "8x+4y=16<BR>\n" );
document.write( "8x+4*(-2)=16<BR>\n" );
document.write( "8x-8=16<BR>\n" );
document.write( "8x=16+8<BR>\n" );
document.write( "8x=24<BR>\n" );
document.write( "x = 24/8<BR>\n" );
document.write( "x = 3<BR>\n" );
document.write( "Or,<BR>\n" );
document.write( "4x-7y=26<BR>\n" );
document.write( "4x-7(-2)=26<BR>\n" );
document.write( "4x+14=26<BR>\n" );
document.write( "4x=26-14<BR>\n" );
document.write( "4x = 12<BR>\n" );
document.write( "x = 12/4<BR>\n" );
document.write( "x = 3<BR>\n" );
document.write( "Or,<BR>\n" );
document.write( "8x-14y=52<BR>\n" );
document.write( "8x-14(-2)=52<BR>\n" );
document.write( "8x+28=52<BR>\n" );
document.write( "8x=52-28<BR>\n" );
document.write( "8x=24<BR>\n" );
document.write( "x = 24/8<BR>\n" );
document.write( "x = 3<BR>\n" );
document.write( "You only need to pick one equation involving x and y in it.\r<BR>\n" );
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document.write( "Solution: x = 3 and y = -2<BR>\n" );
document.write( "This is equivalent to writing (x,y) = (3,-2)\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "Plug those x and y values into the first original equation<BR>\n" );
document.write( "8x+4y=16<BR>\n" );
document.write( "8*3+4*(-2)=16<BR>\n" );
document.write( "24-8=16<BR>\n" );
document.write( "16=16<BR>\n" );
document.write( "That verifies the first original equation.<BR>\n" );
document.write( "Do the same for the second original equation<BR>\n" );
document.write( "4x-7y = 26<BR>\n" );
document.write( "4*3-7*(-2) = 26<BR>\n" );
document.write( "12+14 = 26<BR>\n" );
document.write( "26 = 26<BR>\n" );
document.write( "Both equations are verified. The answer is fully confirmed.<BR>\n" );
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