document.write( "Question 923081: solve this problem using elimination substitution and graphing
\n" ); document.write( " 1)p+3q=16
\n" ); document.write( " p+q=6 \n" ); document.write( "

Algebra.Com's Answer #559863 by MathLover1(20850) $\"\"$ $\"About$

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Elimination/Addition\r
\n" ); document.write( "\n" ); document.write( " $\"p%2B3q=16\"$ .......eq.1
\n" ); document.write( " $\"p%2Bq=6+\"$ .........eq.2
\n" ); document.write( "____________subtract 2 from 1\r
\n" ); document.write( "\n" ); document.write( " $\"p%2B3q-%28p%2Bq%29=16-6\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"cross%28p%29%2B3q-cross%28p%29-q=10\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"3q-q=10\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2q=10\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"highlight%28q=5%29\"$ \r
\n" ); document.write( "\n" ); document.write( "go to $\"p%2Bq=6+\"$ .........eq.2, plug in $\"5\"$ for $\"q\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"p%2B5=6+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"p=6-5+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"highlight%28p=1%29+\"$ \r
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\n" ); document.write( "\n" ); document.write( "by SUBSTITUTION\r
\n" ); document.write( "\n" ); document.write( " $\"p%2B3q=16\"$ .......eq.1
\n" ); document.write( " $\"p%2Bq=6+\"$ .........eq.2
\n" ); document.write( "____________\r
\n" ); document.write( "\n" ); document.write( " $\"p%2B3q=16\"$ .......eq.1..solve for $\"p\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"p=16-3q\"$ ...substitute in 2 \r
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\n" ); document.write( "\n" ); document.write( " $\"16-3q%2Bq=6+\"$ .........eq.2..solve for $\"q\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-2q=6-16+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-2q=-10+\"$ ...both sides multiply by $\"-1\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2q=10+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"highlight%28q=5%29+\"$ ....substitute in eq.1\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"p%2B3%2A5=16\"$ .......eq.1\r
\n" ); document.write( "\n" ); document.write( " $\"p%2B15=16\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"p=16-15\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"highlight%28p=1%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "by Graphing\r
\n" ); document.write( "\n" ); document.write( "In order to graph these equations, we need to solve for q for each equation.\r
\n" ); document.write( "\n" ); document.write( " $\"p%2B3q=16\"$ .......eq.1
\n" ); document.write( " $\"p%2Bq=6+\"$ .........eq.2
\n" ); document.write( "____________\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"3q=-p%2B16\"$ .......eq.1
\n" ); document.write( " $\"q=-p%2B6+\"$ .........eq.2
\n" ); document.write( "____________\r
\n" ); document.write( "\n" ); document.write( " $\"q=-%281%2F3%29p%2B16%2F3\"$ .......eq.1
\n" ); document.write( " $\"q=-p%2B6+\"$ .........eq.2
\n" ); document.write( "____________\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "now find two points that lie on each line\r
\n" ); document.write( "\n" ); document.write( " $\"q=-%281%2F3%29p%2B16%2F3\"$ .......eq.1...set $\"q=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"0=-%281%2F3%29p%2B16%2F3\"$ ...solve for $\"p\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%281%2F3%29p=16%2F3\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"p%2F3=16%2F3\"$ ...if denominator same, numerator must be same too\r
\n" ); document.write( "\n" ); document.write( " $\"p=16\"$ \r
\n" ); document.write( "\n" ); document.write( "point is ( $\"16\"$ , $\"0\"$ )=> x(or p)-intercept\r
\n" ); document.write( "\n" ); document.write( " $\"q=-%281%2F3%29p%2B16%2F3\"$ .......eq.1...set $\"p=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"q=-%281%2F3%290%2B16%2F3\"$ ...solve for $\"p\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"q=16%2F3\"$ \r
\n" ); document.write( "\n" ); document.write( "point is ( $\"0\"$ , $\"16%2F3\"$ )=> y(or q)-intercept\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"q=-p%2B6+\"$ .........eq.2\r
\n" ); document.write( "\n" ); document.write( " $\"q=-p%2B6\"$ .......eq.2...set $\"q=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"0=-p%2B6\"$ ...solve for $\"p\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"p=6\"$ \r
\n" ); document.write( "\n" ); document.write( "point is ( $\"6\"$ , $\"0\"$ )=> x(or p)-intercept\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"q=-p%2B6\"$ .......eq.2...set $\"p=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"q=0%2B6\"$ ...solve for $\"p\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"q=6\"$ \r
\n" ); document.write( "\n" ); document.write( "point is ( $\"0\"$ , $\"6\"$ )=> y(or q)-intercept\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "plot points ( $\"16\"$ , $\"0\"$ ) and ( $\"0\"$ , $\"16%2F3\"$ ) and draw a line $\"q=-%281%2F3%29p%2B16%2F3\"$ \r
\n" ); document.write( "\n" ); document.write( "plot points ( $\"6\"$ , $\"0\"$ ) and ( $\"0\"$ , $\"6\"$ )and draw a line $\"q=-p%2B6\"$ \r
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