document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118051>Question 118051</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618007296/algebrahomeworkh>Advanced Mathematics - precalculus with discrete mathamatics and data analysis</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\">  Find real numbers of x and y such that :\r<BR>\n" );
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document.write( "    (2x+y) + (3-5x)i = 1-7i </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86124 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=86124\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This problem can be solved by recognizing that both the left side and the right side have real<BR>\n" );
document.write( "and imaginary parts that are separate.<BR>\n" );
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document.write( "The real part of the left side is 2x + y and the real part of the right side is 1. These two must<BR>\n" );
document.write( "be equal. So one of the equations that can be written is:<BR>\n" );
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document.write( "2x + y = 1.<BR>\n" );
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document.write( "Next, look at the multipliers of i on both the left and right sides. On the left side the multiplier<BR>\n" );
document.write( "of i is 3 - 5x. On the right side the multiplier of i is -7. These two multipliers must equal<BR>\n" );
document.write( "to make the imaginary parts equal. So another equation that can be written is:<BR>\n" );
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document.write( "3 - 5x = -7<BR>\n" );
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document.write( "Subtract 3 from both sides to get rid of the 3 on the left side and the resulting <BR>\n" );
document.write( "equation is:<BR>\n" );
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document.write( "-5x = -10<BR>\n" );
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document.write( "Solve for x by dividing both sides by -5 and you have:<BR>\n" );
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document.write( "x = -10/-5 = +2<BR>\n" );
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document.write( "Now that x has been found, return to the first equation and substitute +2 for x and solve<BR>\n" );
document.write( "for y. The first equation was:<BR>\n" );
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document.write( "2x + y = 1<BR>\n" );
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document.write( "Substitute +2 for x and this equation becomes:<BR>\n" );
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document.write( "2(2) + y = 1<BR>\n" );
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document.write( "Multiply out the first term on the left side to get:<BR>\n" );
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document.write( "4 + y = 1<BR>\n" );
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document.write( "Get rid of the 4 on the left side by subtracting 4 from both sides. This reduces the equation<BR>\n" );
document.write( "to:<BR>\n" );
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document.write( "y = 1 - 4 = -3<BR>\n" );
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document.write( "So the answers to this problem are: x = +2, y = -3.<BR>\n" );
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document.write( "Check by substituting these two values into the original problem:<BR>\n" );
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document.write( "(2x+y) + (3-5x)i = 1-7i<BR>\n" );
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document.write( "Substitute the values that were found to get:<BR>\n" );
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document.write( "(2(2)+ (-3)) + (3 -5(2))i = 1 - 7i<BR>\n" );
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document.write( "(4 - 3) + (3 - 10)i = 1 - 7i<BR>\n" );
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document.write( "1 - 7i = 1 - 7i<BR>\n" );
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document.write( "Checks out, so the answers are correct: ... x = +2, y = -3.<BR>\n" );
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document.write( "Hope this helps you to understand the problem.  The basic lesson is that the real parts on<BR>\n" );
document.write( "both sides of the equal sign must be equal, and the imaginary parts on both sides of the<BR>\n" );
document.write( "equal sign must also be equal.<BR>\n" );
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document.write( " </SPAN>\n" );
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