document.write( "Question 243708: Solve using the substitution method.\r
\n" ); document.write( "\n" ); document.write( "4m+n=23
\n" ); document.write( "m-4n=10 \n" ); document.write( "

Algebra.Com's Answer #178512 by oberobic(2304) $\"\"$ $\"About$

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With the substitution method, you isolate one unknown and then substitute it into the other equation to find a solution. The equations are:
\n" ); document.write( "EQ1: 4m + n = 23
\n" ); document.write( "EQ2: m - 4n= 10
\n" ); document.write( ".
\n" ); document.write( "Working with EQ2.
\n" ); document.write( "Add 4n to both sides.
\n" ); document.write( "m = 4n + 10
\n" ); document.write( ".
\n" ); document.write( "Now we can substitute it back into EQ1.
\n" ); document.write( "4(4n+10) + n = 23
\n" ); document.write( "Multiply through the left-hand pararentheses
\n" ); document.write( "16n + 40 + n = 23
\n" ); document.write( "Collect like terms
\n" ); document.write( "17n + 40 = 23
\n" ); document.write( "Subtract 40 from both sides
\n" ); document.write( "17n = - 17
\n" ); document.write( "Divide both sides by 17
\n" ); document.write( "n = -1
\n" ); document.write( ".
\n" ); document.write( "Now we take that value and substitute back into EQ2.
\n" ); document.write( "m = 4(-1) + 10
\n" ); document.write( "m = 6
\n" ); document.write( ".
\n" ); document.write( "So our proposed solution is:
\n" ); document.write( "n = -1
\n" ); document.write( "m = 6
\n" ); document.write( ".
\n" ); document.write( "We can check by putting these values back into the equations.
\n" ); document.write( "4(6) + (-1) = 24 - 1 = 23. Check.
\n" ); document.write( "6 - 4(-1) = 6 + 4 = 10. Check. \n" ); document.write( "

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