document.write( "Question 1116936: Helping my son with some algebra stuff. We're struggling with systems of equations. What we're struggling with mostly is 'why' you do the order of operations in the way they are done. Here's the problem:
\n" ); document.write( "a-6=2b
\n" ); document.write( "a+b=15
\n" ); document.write( "The questions calls for the point where the these equations cross (#,#)
\n" ); document.write( "Here's where we are:
\n" ); document.write( "Consolidating the problems: a+2b+a+b=6+15 or 2a+3b=21
\n" ); document.write( "Using the basic y=Mx+b to get slope.
\n" ); document.write( "Now have no clue where to go from here.
\n" ); document.write( "Appreciate the help
\n" ); document.write( "Robert & Jason \n" ); document.write( "

Algebra.Com's Answer #731842 by ikleyn(52832) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "a - 6 = 2b     (1)\r\n" );
document.write( "a + b = 15     (2)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    \"The questions calls for the point where these equations cross (#,#)\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The question CAN NOT be \"for the point where these equations cross (#,#)\".  // Since equations do not cross.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The question can be EITHER to find the intersection point of the two lines (1) and (2) OR to find the common solution to this system of equations.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Both these questions are equivalent.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To solve the system,  express  \"a\" from equation (1):  a = 2b + 6, and then substitute it into equation (2) to get\r\n" );
document.write( "\r\n" );
document.write( "(2b+6) + b = 15\r\n" );
document.write( "\r\n" );
document.write( "3b + 6 = 15\r\n" );
document.write( "\r\n" );
document.write( "3b = 15-6  ====>  3b = 9  ====>  b =  = 3.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now, when you just found the value of b = 3, substitute it into equation (1) to find  a = 2b+6 = 2*3 + 6 = 12.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer.  The solution to the system  is a= 12,  b= 3,  or the pair (a,b) = (12,3).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Check.   Check the solution/(the answer) on your own by substituting the found values into original equations.\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The method I used in the solution is called \"the Substitution method\".\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "It is THE FIRST method that students use when they start learning solving systems of equations.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );