document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191662>Question 1191662</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose a, b, c and d are constants such that a is not a zero and the system below is consistent for all possible values of f and g. What can you say about the numbers a,b,c and d? Justify your answer.\r<BR>\n" );
document.write( "\n" );
document.write( "    ax1 + bx2 = f<BR>\n" );
document.write( "    cx1 + dx2 = g\r<BR>\n" );
document.write( "\n" );
document.write( "I am new to this work, so we have not done as many exercises yet, but we are writing a quiz soon, and will appreciate if you can help me solve this question. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #823477 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52782)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=823477\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Where @MathLover1 copied/pasted her answer, is this link\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "https://math.berkeley.edu/~peyam/Math54Su12/Homeworks/RHW1.pdf\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You will find the solution there &nbsp;(Exercise 1.1.28) &nbsp;in much better format for reading.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Looking at this problem, &nbsp;I'd say that the condition is equivalent to the statement <BR>\n" );
document.write( "that the determinant of the system  &nbsp;&nbsp;(ad - bc)  &nbsp;&nbsp;is not equal to zero.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The particular condition that &nbsp;a =/= 0 &nbsp;is not relevant, &nbsp;at all.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "----------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "On solving systems of two linear equations in two unknowns by the &nbsp;Substitution method, <BR>\n" );
document.write( "Elimination method, &nbsp;determinants' method see the lessons \r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF= http://www.algebra.com/algebra/homework/coordinate/lessons/Solution-of-the-lin-system-of-two-eqns-by-the-Subst-method.lesson>Solution of the linear system of two equations in two unknowns by the Substitution method</A> \r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF= http://www.algebra.com/algebra/homework/coordinate/lessons/Solution-of-the-lin-syst-of-two-eqns-with-two-unknowns-Elimination-method.lesson>Solution of the linear system of two equations in two unknowns by the Elimination method</A> \r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/coordinate/lessons/Solution-of-the-lin-syst-of-two-eqns-with-two-unknowns-using-det.lesson>Solution of the linear system of two equations in two unknowns using determinant</A> \r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/coordinate/lessons/Geom-interpret-of-the-lin-system-of-two-eqns-with-two-unknowns.lesson>Geometric interpretation of the linear system of two equations in two unknowns</A> \r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Useful-tricks-when-solving-systems-of-2-eqns-in-2-unknowns-by-the-Subst-method.lesson>Useful tricks when solving systems of 2 equations in 2 unknowns by the Substitution method</A> \r<BR>\n" );
document.write( "\n" );
document.write( "in this site.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The referred lessons are the part of this online textbook under the topic \"<U>Systems of two linear equations in two unknowns</U>\".\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Save the link to this online textbook together with its description\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Free of charge online textbook in ALGEBRA-I<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "to your archive and use it when it is needed.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );