document.write( "Question 107814: A.Can you please give me an example of a system of equations that is more easily solved by substitution?\r
\n" ); document.write( "\n" ); document.write( "B. Can you give me an example of a system of equations that is more easily to solve by addition? \n" ); document.write( "

Algebra.Com's Answer #78582 by MathLover1(20850) $\"\"$ $\"About$

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1.\r
\n" ); document.write( "\n" ); document.write( "Solve by adding:\r
\n" ); document.write( "\n" ); document.write( " $\"-3x+%2B+5y+=+12\"$
\n" ); document.write( " $\"3x+%2B+2y+=+9\"$ \r
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\n" ); document.write( "\n" ); document.write( "If we add the two equations, we will get $\"0x+%2B+7y+=+21\"$ or $\"7y+=+21\"$ . \r
\n" ); document.write( "\n" ); document.write( "If we divide both sides by $\"7\"$ , we get $\"y+=+3\"$ . \r
\n" ); document.write( "\n" ); document.write( "Next, we substitute $\"3\"$ in for $\"y\"$ into any of given equations. \r
\n" ); document.write( "\n" ); document.write( "If we choose to substitute in the first equation, we get $\"+-3x+%2B+5%283%29+=+12\"$ Е ==> Е $\"-3x+%2B+15+=+12+\"$ Е==>Е $\"+-3x+=+-3\"$ Е ==>Е $\"x+=+1\"$ . \r
\n" ); document.write( "\n" ); document.write( "So the two lines intersect at ( $\"1\"$ , $\"3\"$ ).\r
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\n" ); document.write( "\n" ); document.write( "2.\r
\n" ); document.write( "\n" ); document.write( "Solve a system by substitution \r
\n" ); document.write( "\n" ); document.write( "1st: Pick $\"1\"$ equation and solve for $\"1\"$ of the variables.
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\n" ); document.write( " $\"5x%2B4y=6\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y+=-2x%2B3+\"$ \r
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\n" ); document.write( "The second equation is already solved for $\"y\"$ .
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\n" ); document.write( "\" $\"-2x%2B3\"$ \" is the expression needed.
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\n" ); document.write( "2nd: Substitute this expression in the other equation. \r
\n" ); document.write( "\n" ); document.write( " $\"5x%2B4y+=+6\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"5x+%2B+4%28-2x+%2B+3%29+=+6\"$ \r
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\n" ); document.write( "3rd: Sovle. \r
\n" ); document.write( "\n" ); document.write( " $\"5x%2B4%28-2x%2B3%29=+6\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"5x-8x%2B12=+6\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-3x%2B12=+6\"$ \r
\n" ); document.write( "\n" ); document.write( "Add $\"-12\"$ to the both sides\r
\n" ); document.write( "\n" ); document.write( " $\"-3x%2B12+%96+12+=+6+-+12\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-3x=++-+6\"$ ЕЕ..divide both sides by $\"-3\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-3x%2F%28-3%29+=+-6%2F%28-3%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x+=+2\"$ \r
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\n" ); document.write( "4th: Use this new value in the step $\"1\"$ equation to get the other variable. \r
\n" ); document.write( "\n" ); document.write( " $\"y+=-2x%2B3+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y+=-2%2A2+%2B+3+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y+=+-+4+%2B+3+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y+=+-+1\"$ \r
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\n" ); document.write( "5th: State the solution and include values for both variables. \r
\n" ); document.write( "\n" ); document.write( " $\"x+=+2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+y+=+-1+\"$ \r
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\n" ); document.write( "\n" ); document.write( "So the two lines intersect at ( $\"2\"$ , $\"-1\"$ )\r
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