document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=145136>Question 145136</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could someone please help me with a few problems?These are Systems of equations,and these are solved by the substitution method.<BR>\n" );
document.write( "1)x + y = 15<BR>\n" );
document.write( " 4x + 3y = 38\r<BR>\n" );
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document.write( "2)-3x + y = -4<BR>\n" );
document.write( "    x - y = 0\r<BR>\n" );
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document.write( "Could you please show me step by step on how to work them, because that has helped me so much in the past. I want to thank you so much in advance for all the help you have given me.<BR>\n" );
document.write( "Sincerely,<BR>\n" );
document.write( "Elle J. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #105827 by </B><A HREF=/tutors/aboutme.mpl?userid=algebrapro18><B>algebrapro18(249)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=algebrapro18><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=105827\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Lets first review the steps of substitution.<BR>\n" );
document.write( "1) Solve one of the two equations for a variable(either x or y).<BR>\n" );
document.write( "2) Plug in the thing you just solved for into the other equation and solve for the other variable.<BR>\n" );
document.write( "3) Use your number solution to number 2 to solve for the origonal equation.  <BR>\n" );
document.write( "4) Check your solution.  Both numbers must satisfy both equations to be a solution to the system.<br>\r<BR>\n" );
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document.write( "1)x + y = 15<BR>\n" );
document.write( "4x + 3y = 38<br>\r<BR>\n" );
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document.write( "For this first problem lets solve the top equation for y.<BR>\n" );
document.write( "x + y = 15 --> Subtract x from both sides<BR>\n" );
document.write( "y = -x + 15 <br>\r<BR>\n" );
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document.write( "Now lets plug in that expression into the second equation and solve for x.  <BR>\n" );
document.write( "4x + 3y = 38 --> Substitute y = -x + 15 into the equation<BR>\n" );
document.write( "4x + 3(-x+15) = 38 --> Distribute the 3<BR>\n" );
document.write( "4x + -3x + 45 = 38 --> Combine like terms<BR>\n" );
document.write( "x + 45 = 38 --> Solve for x by subtracting 45 from both sides<BR>\n" );
document.write( "x = -7<br>\r<BR>\n" );
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document.write( "Now Plug x = -7 into the expression we found when we solved the first equation to solve for y.  <BR>\n" );
document.write( "y = -x + 15 --> Plug x = -7 into the expression<BR>\n" );
document.write( "y = -(-7) + 15 --> Simplify and solve for y<BR>\n" );
document.write( "y = 22<br>\r<BR>\n" );
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document.write( "So as you can see we got the answer x = -7 and y = 22.  Now lets check our solution. <BR>\n" );
document.write( "x + y = 15 --> Plug in x = -7 and y = 22<BR>\n" );
document.write( "-7 + 22 = 15 --> Simplify<BR>\n" );
document.write( "15 = 15<br>\r<BR>\n" );
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document.write( "4x + 3y = 38 --> Plug in x = -7 and y = 22<BR>\n" );
document.write( "4(-7) + 3(22) = 38 --> Complete the multiplication<BR>\n" );
document.write( "-28 + 66 = 38 --> Simplify<BR>\n" );
document.write( "38 = 38<br>\r<BR>\n" );
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document.write( "since both equations checked out we know that our solution of x = -7 and y = 22 worked out.  <br>\r<BR>\n" );
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document.write( "2)-3x + y = -4<BR>\n" );
document.write( "x - y = 0<br> \r<BR>\n" );
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document.write( "Here we want to solve the bottom equation for x.  <BR>\n" );
document.write( "x - y = 0 --> Add y to both sides<BR>\n" );
document.write( "x = y<br>\r<BR>\n" );
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document.write( "Now substitute that expression into equation 1 and solve for y.  <BR>\n" );
document.write( "-3x + y = -4 --> Plug y in for x<BR>\n" );
document.write( "-3(y) + y = -4 --> combine like terms<BR>\n" );
document.write( "-2y = -4 --> Divide both sides by -2<BR>\n" );
document.write( "y = 2<br>\r<BR>\n" );
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document.write( "Plug y = 2 into the first expression and solve for x.<BR>\n" );
document.write( "x = 2<br>\r<BR>\n" );
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document.write( "Now we check our solution of x = 2 and y = 2.<br>\r<BR>\n" );
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document.write( "-3x + y = -4 --> Plug x = 2 and y = 2 into the equation<BR>\n" );
document.write( "-3(2) + 2 = -4 --> complete the multiplication<BR>\n" );
document.write( "-6 + 2 = -4 --> Simplify<BR>\n" );
document.write( "-4 = -4<br>\r<BR>\n" );
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document.write( "x - y = 0 --> Plug x = 2 and y = 2 into the equation<BR>\n" );
document.write( "2 - 2 = 0 --> Simplify<BR>\n" );
document.write( "0 = 0<br>\r<BR>\n" );
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document.write( "Since both equations worked out we know that x = 2 and y =2 is our solution. </SPAN>\n" );
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