document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=773372>Question 773372</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the solution to each system by the substitution method. Check your answers.<BR>\n" );
document.write( "3x-5y= -7<BR>\n" );
document.write( "x-4y=-7\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #471657 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=471657\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When solving a system by substitution, you start by solving for one of the variables in one of the equations.<BR>\n" );
document.write( "It is easier if you look for a variable with a coefficient of 1 or -1, meaning that you look for a variable that does not have a number in front, at most it has a + or - sign.<BR>\n" );
document.write( "For example,<BR>\n" );
document.write( "in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-y=2 ALIGN=MIDDLE  ALT=\"2x-y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, it is easiest to solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "while in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4y=5 ALIGN=MIDDLE  ALT=\"x%2B4y=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, it is easiest to solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Solving for the variable gives you an expression for that variable as a function of the other variable(s).<BR>\n" );
document.write( "Then you substitute that expression into the other equation(s).<BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%283x-5y=+-7%2Cx-4y=-7%29 ALIGN=MIDDLE  ALT=\"system%283x-5y=+-7%2Cx-4y=-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-4y=-7 ALIGN=MIDDLE  ALT=\"x-4y=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > is easiest:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-4y=-7 ALIGN=MIDDLE  ALT=\"x-4y=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4y-7 ALIGN=MIDDLE  ALT=\"x=4y-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > (adding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y ALIGN=MIDDLE  ALT=\"4y\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides of the equal sign.<BR>\n" );
document.write( "Next we substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y-7 ALIGN=MIDDLE  ALT=\"4y-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-5y=+-7 ALIGN=MIDDLE  ALT=\"3x-5y=+-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%284y-7%29-5y=+-7 ALIGN=MIDDLE  ALT=\"3%284y-7%29-5y=+-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A4y-3%2A7-5y=+-7 ALIGN=MIDDLE  ALT=\"3%2A4y-3%2A7-5y=+-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > (applying the distributive property)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A4y-3%2A7-5y=+-7 ALIGN=MIDDLE  ALT=\"3%2A4y-3%2A7-5y=+-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12y-21-5y=+-7 ALIGN=MIDDLE  ALT=\"12y-21-5y=+-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > (doing the indicated operations)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12y-21-5y=+-7 ALIGN=MIDDLE  ALT=\"12y-21-5y=+-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12y-5y=+-7%2B21 ALIGN=MIDDLE  ALT=\"12y-5y=+-7%2B21\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12y-5y=14 ALIGN=MIDDLE  ALT=\"12y-5y=14\"   DISABLED_style= \"max-width:90%; height:auto;\" > (adding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21 ALIGN=MIDDLE  ALT=\"21\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12y-5y=14 ALIGN=MIDDLE  ALT=\"12y-5y=14\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812-5%29y=14 ALIGN=MIDDLE  ALT=\"%2812-5%29y=14\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7y=14 ALIGN=MIDDLE  ALT=\"7y=14\"   DISABLED_style= \"max-width:90%; height:auto;\" > (taking out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > as a common factor, sometimes called \"collecting like terms\")<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7y=14 ALIGN=MIDDLE  ALT=\"7y=14\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=14%2F7 ALIGN=MIDDLE  ALT=\"y=14%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=2%29 ALIGN=MIDDLE  ALT=\"highlight%28y=2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (dividing both sides by 7)<BR>\n" );
document.write( "Now we substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the solved-for-x equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4y-7 ALIGN=MIDDLE  ALT=\"x=4y-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > above:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4%2A2-7 ALIGN=MIDDLE  ALT=\"x=4%2A2-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8-7 ALIGN=MIDDLE  ALT=\"x=8-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=1%29 ALIGN=MIDDLE  ALT=\"highlight%28x=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "Checking the answer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28system%28x=1%2Cy=2%29%29 ALIGN=MIDDLE  ALT=\"highlight%28system%28x=1%2Cy=2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-5y=3%2A1-5%2A2=3-10=-7 ALIGN=MIDDLE  ALT=\"3x-5y=3%2A1-5%2A2=3-10=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > verifies <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-5y=-7 ALIGN=MIDDLE  ALT=\"3x-5y=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-4y=1-4%2A2=1-8=-7 ALIGN=MIDDLE  ALT=\"x-4y=1-4%2A2=1-8=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > verifies <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-4y=-7 ALIGN=MIDDLE  ALT=\"x-4y=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );