document.write( "Question 1043938: Solve the system using the substitution method. If the system has no solution or an infinite number of solutions, state this.\r
\n" ); document.write( "\n" ); document.write( "x+y=7
\n" ); document.write( "6x+6y=42
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #659169 by MathTherapy(10552) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "Solve the system using the substitution method. If the system has no solution or an infinite number of solutions, state this.\r
\n" ); document.write( "\n" ); document.write( "x+y=7
\n" ); document.write( "6x+6y=42
\n" ); document.write( "

x + y = 7 ----- eq (i)
\n" );
document.write( "6x + 6y = 42 ------ eq (ii)
\n" );
document.write( "Multiply eq (i) by 6 to get the exact equation as eq (ii)
\n" );
document.write( "Divide eq (ii) by 6 to get the exact equation as eq (i)
\n" );
document.write( "This means the equations are the SAME, and therefore there is an .\r
\n" );
document.write( "\n" );
document.write( "However, you have to determine the answer using the SUBSTITUTION method. we then get: 
\n" );
document.write( "x + y = 7____x = 7 - y ------ eq (i)
\n" );
document.write( "6x + 6y = 42 ------- eq (ii)
\n" );
document.write( "6(7 - y) + 6y = 42 -------- Substituting 7 - y for x in eq (ii)
\n" );
document.write( "42 - 6y + 6y = 42
\n" );
document.write( "- 6y + 6y = 42 - 42
\n" );
document.write( "0 = 0 ----- This is a TRUE statement and so, there is an:  . \n" );
document.write( "

\n" );