![\"\"](\"/images/stars/stars-13.gif\")
You can put this solution on YOUR website!
The key to the addition/elimination process (aka Linear Combination) is to get opposites for one of the variable in the two equations. There are more clever ways to accomplish this but one way would be:
- Line up the variables by getting the two equations into the form Ax + By = C.
- Multiply the second equation by the first coefficient of the first equation.
- Multiply the first equation by the negative of the first coefficient of the second equation.
- At this point you should have opposites for the first variable
\n" ); document.write( "Let's see this \"in action\":
\n" ); document.write( "1. Line up the variables. Both your equations are already in Ax + By = C form so there is nothing to do yet.
\n" ); document.write( "2. Multiply the second equation.... The first equation's first coefficient is 7 so we will multiply both sides of the second equation by 7:
\n" ); document.write( "7(8p-9q) = 7(17)
\n" ); document.write( "56p - 63q = 119
\n" ); document.write( "3. Multiply the first equation.... The second equation's first coefficient is 8. The negative of 8 is -8. So we will multiply the first equation by -8:
\n" ); document.write( "-8(7p+5q) = -8(2)
\n" ); document.write( "-56p - 40q = -16
\n" ); document.write( "Now our system looks like:
\n" ); document.write( "56p - 63q = 119
\n" ); document.write( "-56p - 40q = -16
\n" ); document.write( "And, as you can see, we have opposite p terms. Once we have opposites the rest is fairly simple: Add the two equations (the opposite terms cancel out):
\n" ); document.write( "-103q = 103
\n" ); document.write( "Solve:
\n" ); document.write( "q = -1
\n" ); document.write( "Use this value in one of the original equations to find the other variable:
\n" ); document.write( "7p + 5(-1) = 2
\n" ); document.write( "7p + (-5) = 2
\n" ); document.write( "7p = 7
\n" ); document.write( "p = 1 \n" ); document.write( "