document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=62013>Question 62013</A>: <I><SPAN STYLE=\"word-break: break-all;\"> On number 1 I tried to use the calculator on the help page, but I didn't understand how they did it.  And for number 2 I read what they had written as the description and read it over and over and looked in the book, but I was still lost and confused. \r<BR>\n" );
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document.write( "(1) Solve each of the following systems. <BR>\n" );
document.write( "(a) x + 2y = -6<BR>\n" );
document.write( "    x - 2y = 14\r<BR>\n" );
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document.write( "(b) 3a - b = 0<BR>\n" );
document.write( "    a + 2b 7/2\r<BR>\n" );
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document.write( "(2) The equation of a straight line can be found if you are given the coordinates of two points on the line.  One way to do this is to use systems of equations.  The slope-intercept form for a linear equation is y = mx + b.  Each point on a line must make the equation true when the coordinates are substituted for x and y.  As each point is substituted, a seperate linear equation is formed; the two points produce two equations with variables m and b.  Solving the system gives you the value of m and b and , thus, the equation of the line. \r<BR>\n" );
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document.write( "For each of the following pairs of points, find the line which would contain each pair.<BR>\n" );
document.write( "(a) (-2, 3) and (1,9)\r<BR>\n" );
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document.write( "(b) (1/3, 2/5) and (5/3 , 1)\r<BR>\n" );
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document.write( "(c) (5, -24) and (1, 14)\r<BR>\n" );
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document.write( "(d) (3, squareroot 2) and (1, 3 sqauareroot 2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #42791 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=42791\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (1) Solve each of the following systems. <BR>\n" );
document.write( "(a) <BR>\n" );
document.write( "1st: x + 2y = -6<BR>\n" );
document.write( "2nd: x - 2y = 14<BR>\n" );
document.write( "Subtract the 1st from the 2nd to get:<BR>\n" );
document.write( "-4y=20<BR>\n" );
document.write( "y=-5<BR>\n" );
document.write( "Substitute that into 2nd to solve for y as follows:<BR>\n" );
document.write( "x-2*-5=14<BR>\n" );
document.write( "x+10=14<BR>\n" );
document.write( "x=4<BR>\n" );
document.write( "Check in 1st as follows:<BR>\n" );
document.write( "4+2(-5)=-6<BR>\n" );
document.write( "4-10=-6<BR>\n" );
document.write( "-6=-6<BR>\n" );
document.write( "SOLUTION:<BR>\n" );
document.write( "x=4,y=-5<BR>\n" );
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document.write( "(b) <BR>\n" );
document.write( "1st: 3a - b = 0<BR>\n" );
document.write( "2nd:  a + 2b =7/2 <BR>\n" );
document.write( "Multiply 1st be 2 to get:<BR>\n" );
document.write( "3rd: 6a-2b=0<BR>\n" );
document.write( "Add 2nd and 3rd to get:<BR>\n" );
document.write( "7a=7/2<BR>\n" );
document.write( "a=1/2<BR>\n" );
document.write( "Substitute into 2nd to solve for \"a\", as follows:<BR>\n" );
document.write( "1/2 +2b = 7/2<BR>\n" );
document.write( "2b=3<BR>\n" );
document.write( "b=(3/2)<BR>\n" );
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document.write( "Check in 1st as follows:<BR>\n" );
document.write( "3(1/2)-(3/2)=0<BR>\n" );
document.write( "0=0<BR>\n" );
document.write( "--------------------\r<BR>\n" );
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document.write( "(2) The equation of a straight line can be found if you are given the coordinates of two points on the line. One way to do this is to use systems of equations. The slope-intercept form for a linear equation is y = mx + b. Each point on a line must make the equation true when the coordinates are substituted for x and y. As each point is substituted, a seperate linear equation is formed; the two points produce two equations with variables m and b. Solving the system gives you the value of m and b and , thus, the equation of the line. <BR>\n" );
document.write( "For each of the following pairs of points, find the line which would contain each pair.<BR>\n" );
document.write( "(a) (-2, 3) and (1,9)<BR>\n" );
document.write( "1st: 3=-2m+b<BR>\n" );
document.write( "2nd: 9= m+b<BR>\n" );
document.write( "Subtract 2nd from 1st to get:<BR>\n" );
document.write( "-6=-3m<BR>\n" );
document.write( "m=2<BR>\n" );
document.write( "Substitute into 2nd to solve for b, as follows:<BR>\n" );
document.write( "9=2+b<BR>\n" );
document.write( "b=7<BR>\n" );
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document.write( "Check in 1st as follows:<BR>\n" );
document.write( "3=-2*2+7<BR>\n" );
document.write( "3=-4+7<BR>\n" );
document.write( "3=3<BR>\n" );
document.write( "EQUATION:<BR>\n" );
document.write( "y=2x+7<BR>\n" );
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document.write( "Comment:<BR>\n" );
document.write( "Follow the same procedure to find the proper<BR>\n" );
document.write( "equation for the following problems.<BR>\n" );
document.write( "(b) (1/3, 2/5) and (5/3 , 1) <BR>\n" );
document.write( "(c) (5, -24) and (1, 14) \r<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "(d) (3, squareroot 2) and (1, 3 sqauareroot 2)\r<BR>\n" );
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document.write( "Com<BR>\n" );
document.write( " </SPAN>\n" );
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