document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=258303>Question 258303</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Sloving a system of Linear equation find the value of x and y. can someone please show me the steps I need to be able to capture the information. Thanking you in advance,.\r<BR>\n" );
document.write( "\n" );
document.write( "-7x -6y = 10 <BR>\n" );
document.write( " 3x - 2y = 14? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #190144 by </B><A HREF=/tutors/aboutme.mpl?userid=jmorgan22><B>jmorgan22(8)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jmorgan22><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=190144\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I solved this in the long way to help you understand Solving Linear Equations by Substitution.  I hope this helps.  Have a great day.\r<BR>\n" );
document.write( "\n" );
document.write( "-7x-6y=10 <BR>\n" );
document.write( "3x-2y=14 \r<BR>\n" );
document.write( "\n" );
document.write( "Since -6y does not contain the variable to solve for, move it to the right-hand side of the equation by adding 6y to both sides. \r<BR>\n" );
document.write( "\n" );
document.write( "-7x=6y+10 <BR>\n" );
document.write( "3x-2y=14\r<BR>\n" );
document.write( "\n" );
document.write( "Divide each term in the equation by -7. \r<BR>\n" );
document.write( "\n" );
document.write( "-7x/-7=6y/-7+10/-7<BR>\n" );
document.write( "3x-2y=14 \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Simplify the left-hand side of the equation by canceling the common factors. \r<BR>\n" );
document.write( "\n" );
document.write( "x=6y/-7+10/-7<BR>\n" );
document.write( "3x-2y=14 \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Simplify the right-hand side of the equation by simplifying each term. \r<BR>\n" );
document.write( "\n" );
document.write( "x=-6y-10/7<BR>\n" );
document.write( "3x-2y=14 \r<BR>\n" );
document.write( "\n" );
document.write( "Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is (-6y-10)/7\r<BR>\n" );
document.write( "\n" );
document.write( "x=-6y-10/7<BR>\n" );
document.write( "3(-6y-10/7)-2y=14\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Remove the parentheses around the expression -6y-10. \r<BR>\n" );
document.write( "\n" );
document.write( "x=-6y-10/7<BR>\n" );
document.write( "3(-6y-10/7)-2y=14\r<BR>\n" );
document.write( "\n" );
document.write( "Divide each term in the numerator by the denominator. <BR>\n" );
document.write( "x=-6y/7 – 10/7<BR>\n" );
document.write( "3(-6y-10/7)-2y=14\r<BR>\n" );
document.write( "\n" );
document.write( "Remove the parentheses around the expression -6y-10. \r<BR>\n" );
document.write( "\n" );
document.write( "x=-6y/7 – 10/7<BR>\n" );
document.write( "3(-6y-10/7) – 2y=14\r<BR>\n" );
document.write( "\n" );
document.write( "Divide each term in the numerator by the denominator. \r<BR>\n" );
document.write( "\n" );
document.write( "x=-6y/7 – 10/7<BR>\n" );
document.write( "3(-6y/7 – 10/7) – 2y = 14\r<BR>\n" );
document.write( "\n" );
document.write( "Combine the numerators of all expressions that have common denominators. \r<BR>\n" );
document.write( "\n" );
document.write( "x=-6y/7 – 10/7<BR>\n" );
document.write( "3(-6y – 10/7) – 2y=14\r<BR>\n" );
document.write( "\n" );
document.write( "Multiply 3 by each term inside the parentheses. \r<BR>\n" );
document.write( "\n" );
document.write( "x=-6y/7 – 10/7<BR>\n" );
document.write( "- 6(3y+5)/7 – 2y = 14\r<BR>\n" );
document.write( "\n" );
document.write( "Multiply -6 by each term inside the parentheses. \r<BR>\n" );
document.write( "\n" );
document.write( "x=-6y/7 – 10/7<BR>\n" );
document.write( "-18y – 30/7 – 2y = 14<BR>\n" );
document.write( "Divide each term in the numerator by the denominator. \r<BR>\n" );
document.write( "\n" );
document.write( "x=-6y/7 – 10/7<BR>\n" );
document.write( "-18y/7 – 30/7 – 2y = 14<BR>\n" );
document.write( "Combine the numerators of all expressions that have common denominators. \r<BR>\n" );
document.write( "\n" );
document.write( "x=-6y/7 – 10/7<BR>\n" );
document.write( "-18y -30/7 – 2y = 14\r<BR>\n" );
document.write( "\n" );
document.write( "Factor out the GCF of -6 from each term in the polynomial. \r<BR>\n" );
document.write( "\n" );
document.write( "x=-6y/7 – 10/7<BR>\n" );
document.write( "-6(3y) -6(5)/7 – 2y = 14\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Factor out the GCF of -6 from -18y-30. \r<BR>\n" );
document.write( "\n" );
document.write( "x=-6y/7 – 10/7<BR>\n" );
document.write( "-6(3y+5)/7 – 2y = 14\r<BR>\n" );
document.write( "\n" );
document.write( "Move the -1 to the front of the fraction. \r<BR>\n" );
document.write( "\n" );
document.write( "x=-6y/7 – 10/7<BR>\n" );
document.write( "- 6(3y+5)/7 – 2y = 14\r<BR>\n" );
document.write( "\n" );
document.write( "Multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of 7. \r<BR>\n" );
document.write( "\n" );
document.write( "x=-6y/7 – 10/7<BR>\n" );
document.write( "- 6(3y+5)/7 -2y* 7/7 = 14\r<BR>\n" );
document.write( "\n" );
document.write( "Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 7. \r<BR>\n" );
document.write( "\n" );
document.write( "x=-6y/7 – 10/7<BR>\n" );
document.write( "- 6(3y+5)/7 – 2y*7/7 = 14\r<BR>\n" );
document.write( "\n" );
document.write( "Multiply 2y by 7 to get 14y. \r<BR>\n" );
document.write( "\n" );
document.write( "x=-6y/7 – 10/7<BR>\n" );
document.write( "- 6(3y+5)/7 – 14y/7 = 14<BR>\n" );
document.write( "The numerators of expressions that have equal denominators can be combined. In this case,- 6(3y+5)/7 and – (14y/7) have the same denominator of 7, so the numerators can be combined. \r<BR>\n" );
document.write( "\n" );
document.write( "x=-6y/7 – 10/7<BR>\n" );
document.write( "-6(3y+5) – (14y)/7 =14<BR>\n" );
document.write( "Simplify the numerator of the expression. \r<BR>\n" );
document.write( "\n" );
document.write( "x=-6y/7 – 10/7<BR>\n" );
document.write( "-18y-30-14y/7 = 14<BR>\n" );
document.write( "Since -18y and -14y are like terms, subtract 14y from -18y to get -32y. \r<BR>\n" );
document.write( "\n" );
document.write( "x=-6y/7 – 10/7<BR>\n" );
document.write( "-32y-30/7 = 14\r<BR>\n" );
document.write( "\n" );
document.write( "Factor out the GCF of -2 from each term in the polynomial. \r<BR>\n" );
document.write( "\n" );
document.write( "x=-6y/7 – 10/7<BR>\n" );
document.write( "-2(16y) – 2(15)/7 = 14\r<BR>\n" );
document.write( "\n" );
document.write( "Factor out the GCF of -2 from -32y-30. \r<BR>\n" );
document.write( "\n" );
document.write( "x=-6y/7 – 10/7<BR>\n" );
document.write( "-2(16y+15)/7 = 14\r<BR>\n" );
document.write( "\n" );
document.write( "Remove the parentheses from the numerator. \r<BR>\n" );
document.write( "\n" );
document.write( "x=-6y/7 – 10/7<BR>\n" );
document.write( "- 2(16y+15)/7 = 14\r<BR>\n" );
document.write( "\n" );
document.write( "Multiply each term in the equation by 7. \r<BR>\n" );
document.write( "\n" );
document.write( "x=-6y/7 – 10/7<BR>\n" );
document.write( "- 2(16y+15)/7 * 7=14* 7\r<BR>\n" );
document.write( "\n" );
document.write( "Simplify the left-hand side of the equation by canceling the common factors and Multiply 14 by 7 to get 98.. \r<BR>\n" );
document.write( "\n" );
document.write( "x=-6y/7 – 10/7<BR>\n" );
document.write( "-2(16y+15)=98\r<BR>\n" );
document.write( "\n" );
document.write( "Divide each term in the equation by 2. \r<BR>\n" );
document.write( "\n" );
document.write( "x=-6y/7 – 10/7<BR>\n" );
document.write( "- 2(16y+15)/2 = 98/2\r<BR>\n" );
document.write( "\n" );
document.write( "Simplify the left-hand side of the equation by canceling the common factors. \r<BR>\n" );
document.write( "\n" );
document.write( "x=-6y/7 – 10/7<BR>\n" );
document.write( "-(16y+15)=49 \r<BR>\n" );
document.write( "\n" );
document.write( "Multiply -1 by each term inside the parentheses. <BR>\n" );
document.write( "x=-6y/7 – 10/7<BR>\n" );
document.write( "-16y-15=49 \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since -15 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 15 to both sides. <BR>\n" );
document.write( "x=-6y/7 – 10/7<BR>\n" );
document.write( "-16y=15+49 \r<BR>\n" );
document.write( "\n" );
document.write( "Add 49 to 15 to get 64. \r<BR>\n" );
document.write( "\n" );
document.write( "x=-6y/7 – 10/7<BR>\n" );
document.write( "-16y=64 \r<BR>\n" );
document.write( "\n" );
document.write( "Divide each term in the equation by -16. \r<BR>\n" );
document.write( "\n" );
document.write( "x=-6y/7 – 10/7<BR>\n" );
document.write( "-16y/-16 =64/-16\r<BR>\n" );
document.write( "\n" );
document.write( "Simplify the left-hand side of the equation by canceling the common factors. \r<BR>\n" );
document.write( "\n" );
document.write( "x= -6y/7 – 10/<BR>\n" );
document.write( "y = - 4<BR>\n" );
document.write( "Simplify the right-hand side of the equation by simplifying each term. \r<BR>\n" );
document.write( "\n" );
document.write( "x = -6y/7 – 10/7<BR>\n" );
document.write( "y =- 4 \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );