document.write( "Question 1134702: Solve the equations using elimination and substitution
\n" ); document.write( "（1）2x+3y=11
\n" ); document.write( "4x+y=12
\n" ); document.write( "（2）3x+2y=24
\n" ); document.write( "2x-3y=42 \n" ); document.write( "

Algebra.Com's Answer #752177 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( " $\"2x%2B3y=11\"$ .....eq.1
\n" ); document.write( " $\"4x%2By=12\"$ ......eq.2
\n" ); document.write( "------------------------
\n" ); document.write( "start with\r
\n" ); document.write( "\n" ); document.write( " $\"4x%2By=12\"$ ......eq.2...solve for $\"y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=-4x%2B12\"$ .......eq.2a...substitute in eq.1 to eliminate variable $\"y\"$ \r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"2x%2B3%28-4x%2B12%29=11\"$ .....eq.1\r
\n" ); document.write( "\n" ); document.write( " $\"2x-12x%2B36=11\"$ ...solve for $\"x\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-10x%2B36=11\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-11%2B36=10x\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"25=10x\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"25%2F10=x\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=5%2F2\"$ \r
\n" ); document.write( "\n" ); document.write( "go back to eq.2a, substitute $\"5%2F2\"$ for $\"x\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=-4%2A%285%2F2%29%2B12\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=-10%2B12\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=2\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "solution is intersection point ( $\"x\"$ , $\"y\"$ )=( $\"5%2F2\"$ , $\"2\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"3x%2B2y=24\"$ .......eq.1
\n" ); document.write( " $\"2x-3y=42\"$ .......eq.2
\n" ); document.write( "---------------------------\r
\n" ); document.write( "\n" ); document.write( "start with\r
\n" ); document.write( "\n" ); document.write( " $\"3x%2B2y=24\"$ .......eq.1 ..solve for $\"y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2y=-3x%2B24\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=-3x%2F2%2B24%2F2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=-3x%2F2%2B12\"$ ...........eq.1a\r
\n" ); document.write( "\n" ); document.write( "go to
\n" ); document.write( " $\"2x-3y=42\"$ .......eq.2...substitute in $\"y\"$ from eq.1a to eliminate variable $\"y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2x-3%28-3x%2F2%2B12%29=42\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2x%2B9x%2F2-36=42\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2x%2B9x%2F2=42%2B36\"$ .........both sides multiply by $\"2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"4x%2B9x=84%2B72\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"13x=156\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=156%2F13\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=12\"$ \r
\n" ); document.write( "\n" ); document.write( "go back to eq.1a\r
\n" ); document.write( "\n" ); document.write( " $\"y=-3x%2F2%2B12\"$ ...........eq.1a substitute $\"12\"$ for $\"x\"$ and solve for $\"y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=-%283%2A12%29%2F2%2B12\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=-%283%2Across%2812%296%29%2Fcross%282%29%2B12\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=-3%2A6%2B12\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=-18%2B12\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=-6\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "solution is intersection point ( $\"x\"$ , $\"y\"$ )=( $\"12\"$ , $\"-6\"$ )\r
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\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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