document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203037>Question 1203037</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use algebraic rules of equations to predict the solution type to the system of equations<BR>\n" );
document.write( "f(x)={x+y=-4 y=2x-1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838270 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=838270\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> here's what i get.<BR>\n" );
document.write( "your equations that need to be solve simultaneously are:<BR>\n" );
document.write( "x + y = -4<BR>\n" );
document.write( "y = 2x - 1<BR>\n" );
document.write( "we'll use the substitution method.<BR>\n" );
document.write( "in the first equation, replace y with 2x - 1 from the second equation to get:<BR>\n" );
document.write( "x + 2x - 1 = -4<BR>\n" );
document.write( "add 1 to both sides of the eeuation and combine like terms to get:<BR>\n" );
document.write( "3x = -3<BR>\n" );
document.write( "solve for x to get x = 1-1<BR>\n" );
document.write( "in the second equation, replace x with -1 and solve for y to get:<BR>\n" );
document.write( "y = 2*-1 - 1 = -3<BR>\n" );
document.write( "your solution to this equation is x = -1 and y = -3<BR>\n" );
document.write( "replace x with -1 and y with -3 in both equations to ge:<BR>\n" );
document.write( "x + y = -4 becomes -1 + -3 = -4 which becomes -4 = -4 which is true.<BR>\n" );
document.write( "y = 2x - 1 becomes -3 = 2*-1 - 1 which becomes -2 -1 = -3 which becomes -3 = -3 which is true.<BR>\n" );
document.write( "both equations are true when x = -1 and y = -3.<BR>\n" );
document.write( "the graph of these equations is shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/071401.jpg\">\r<BR>\n" );
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document.write( "A system of simultaneous linear equations can have either: one unique solution, infinitely many solutions or no solutions.\r<BR>\n" );
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document.write( "from a graphical standpoint, the unique solution is where the lines intersect; infinitely many solution are when the lines are identical, i.e. both equations form the same equivalent equation which generates the same line for both; no solutions are whn the lines are parallel to each other.\r<BR>\n" );
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document.write( "theee are ptjer waus to describe the solutions as noted in the following reference.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://ionamaths.weebly.com/uploads/1/4/2/0/14204419/consistencyanddependency.pdf\" target = \"_blank\">https://ionamaths.weebly.com/uploads/1/4/2/0/14204419/consistencyanddependency.pdf</a>\r<BR>\n" );
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document.write( "i think that about covers it.<BR>\n" );
document.write( "let me know if you need more.<BR>\n" );
document.write( "theo\r<BR>\n" );
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