document.write( "Question 577732: Ok so we are doing these problems where you have to find x and y and the equations are 4x+3y=9 and the other one is 3x+4y=12 and what I did was I multiplied 4x+3y=9 and -3 and then i multiplied 3x+4y=12 and 4. But my question is would you multiply the 9 and 12 to? Or would you just multiply the equations? And did I multply by the right numbers? \n" ); document.write( "

Algebra.Com's Answer #370279 by KMST(5328) $\"\"$ $\"About$

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So you have the system of linear equations
\n" ); document.write( " $\"system%284x%2B3y=9%2C3x%2B4y=12%29\"$
\n" ); document.write( "and you are trying to solve it by \"elimination.\"
\n" ); document.write( " $\"4x%2B3y=9\"$ is equivalent to $\"%28-3%29%284x%2B3y%29=%28-3%29%2A9\"$ --> $\"-12x-9y=-27\"$
\n" ); document.write( "If the expression $\"4x%2B3y\"$ is equal to $\"9\"$ ,
\n" ); document.write( "the value of (-3) times that expression will be (-3) times $\"9\"$ .
\n" ); document.write( "Multiplying both sides of the equation by the same non-zero number, gives you another equivalent equation, with exactly the same solutions.
\n" ); document.write( " $\"3x%2B4y=12\"$ is equivalent to $\"4%283x%2B4y%29=4%2A12\"$ --> $\"12x%2B16y=48\"$
\n" ); document.write( "If you did those transformations and got the equivalent equations
\n" ); document.write( " $\"-12x-9y=-27\"$ and $\"12x%2B16y=48%29\"$ ,
\n" ); document.write( "you are on the right path.
\n" ); document.write( "Next you would add those equations and keep the resulting equation
\n" ); document.write( " $\"-12x-9y%2B12x%2B16y=-27%2B48%29\"$ --> $\"7y=21\"$ --> $\"highlight%28y=3%29\"$
\n" ); document.write( "along with one of your original equations:
\n" ); document.write( " $\"system%28y=3%2C4x%2B3y=9%29\"$
\n" ); document.write( "At that point, you would substitute the value of $\"y\"$ into the second equation and find that $\"highlight%28x=0%29\"$ \n" ); document.write( "

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