document.write( "Question 814634: Solve by substitution 3x+2y=12
\n" ); document.write( " x+y=3. How do I do this
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #490411 by LinnW(1048) $\"\"$ $\"About$

You can put this solution on YOUR website!
Solve one of the equations for either x or y in relation to the other.
\n" ); document.write( "For example:\r
\n" ); document.write( "\n" ); document.write( "x+y=3
\n" ); document.write( "Subtract y from each side
\n" ); document.write( "x=-y+3\r
\n" ); document.write( "\n" ); document.write( "Now we can substitute -y+3 for x in the other equation, so
\n" ); document.write( "3x+2y=12 becomes
\n" ); document.write( "3(-y+3) + 2y = 12
\n" ); document.write( "-3y + 9 + 2y = 12
\n" ); document.write( "-y + 9 = 12
\n" ); document.write( "Subtract 9 from each side
\n" ); document.write( "-y = 12 -9
\n" ); document.write( "-y = 3
\n" ); document.write( "Multiply each side by -1
\n" ); document.write( "-1(-y) = -1(3)
\n" ); document.write( "y = -3
\n" ); document.write( "To find the value of x, use our equation x=-y+3
\n" ); document.write( "x= -(-3)+3
\n" ); document.write( "x= 3 + 3
\n" ); document.write( "x=6
\n" ); document.write( "So we have y = -3 and x = 6\r
\n" ); document.write( "\n" ); document.write( "Check these values in the original equations.
\n" ); document.write( "3x+2y=12, doing the substitution
\n" ); document.write( "3(6)+2(-3)=12
\n" ); document.write( "18 -6 =12 , so the first equation checks out.\r
\n" ); document.write( "\n" ); document.write( "x+y=3
\n" ); document.write( "6+(-3)=3
\n" ); document.write( "6-3=3, so the second equation checks out. \n" ); document.write( "

\n" );