document.write( "Question 19970: elimination method\r
\n" ); document.write( "\n" ); document.write( "3x+2y=-24; 4x+3y=18\r
\n" ); document.write( "\n" ); document.write( "5x-4y=-114; 2x+6y=-57 \n" ); document.write( "
Algebra.Com's Answer #9631 by glabow(165)\"\" \"About 
You can put this solution on YOUR website!
I assume your equation pairs read across. Let's take the first one. Elimination means eliminating one of the unknown variables by getting a common coefficient for it in both equations and then subtracting the two sets of equals from each other. [Remember: equals subtracted from equals gives equals.]
\n" ); document.write( "We have
\n" ); document.write( "3x + 2y = -24
\n" ); document.write( "4x + 3y = 18\r
\n" ); document.write( "\n" ); document.write( "We can make the y terms have the same coefficient by multiplying the first equation by 3 and multiplying the second equation by 2. That will make both equations have 6y as the y-term.
\n" ); document.write( "This gives
\n" ); document.write( "9x + 6y = -72
\n" ); document.write( "8x + 6y = 36\r
\n" ); document.write( "\n" ); document.write( "Now we subtract the second equation from the first.
\n" ); document.write( "This leaves
\n" ); document.write( "x = -108\r
\n" ); document.write( "\n" ); document.write( "Since we now know x, we can put that value into either of the original equations and solve for y.
\n" ); document.write( "3(-108) + 2y = -24
\n" ); document.write( "-324 + 2y = -24
\n" ); document.write( "2y = -24 +324 = 300
\n" ); document.write( "y = 150 \r
\n" ); document.write( "\n" ); document.write( "Checking with x=-108 and y=150 shows this to be correct.\r
\n" ); document.write( "\n" ); document.write( "Now you do the second set. [Hint: multiply the first equation by 6 and the second one by 4 and both equations will have 24 for the coefficient of y. In this case one will be positive and the other negative so you can ADD the equations together to get rid of the y-term.]
\n" ); document.write( " \n" ); document.write( "
\n" );