document.write( "Question 149120: Solve each system by substitution\r
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\n" ); document.write( "\n" ); document.write( "1)y=2x-8
\n" ); document.write( "4x+3y=1\r
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\n" ); document.write( "\n" ); document.write( "2)y=x-5
\n" ); document.write( "3x-4(y-2)=28-x\r
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Algebra.Com's Answer #109463 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
1. $\"y=2x-8\"$
\n" ); document.write( "2. $\"4x%2B3y=1\"$
\n" ); document.write( "In the substitution method, you use one equation to get an expression of one variable in terms of the other variable.
\n" ); document.write( "You then substitute this value into the remaining equation.
\n" ); document.write( "In the first case, y is already in terms of x in eq. 1.
\n" ); document.write( "Substitute this expression for y in eq. 2 and solve for x.
\n" ); document.write( "2. $\"4x%2B3y=1\"$
\n" ); document.write( " $\"4x%2B3%282x-8%29=1\"$
\n" ); document.write( " $\"4x%2B6x-24=1\"$
\n" ); document.write( " $\"10x-24=1\"$
\n" ); document.write( " $\"10x=25\"$
\n" ); document.write( " $\"x=25%2F10\"$
\n" ); document.write( " $\"x=5%2F2\"$
\n" ); document.write( "Now use this in either eq. 1 or 2 to get y.
\n" ); document.write( "1. $\"y=2x-8\"$
\n" ); document.write( " $\"y=2%285%2F2%29-8\"$
\n" ); document.write( " $\"y=5-8\"$
\n" ); document.write( " $\"y=-3\"$
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\n" ); document.write( "1. $\"y=x-5\"$
\n" ); document.write( "2. $\"3x-4%28y-2%29=28-x\"$
\n" ); document.write( "Similarly,
\n" ); document.write( "2. $\"3x-4%28y-2%29=28-x\"$
\n" ); document.write( " $\"3x-4%28x-5-2%29=28-x\"$
\n" ); document.write( " $\"3x-4%28x-7%29=28-x\"$
\n" ); document.write( " $\"3x-4x%2B28=28-x\"$
\n" ); document.write( " $\"3x-4x%2B28=28-x\"$
\n" ); document.write( " $\"-x%2B28=-x%2B28\"$
\n" ); document.write( " $\"0=0\"$
\n" ); document.write( "True, but not helpful for a solution.
\n" ); document.write( "When this happens, eq. 1 and eq. 2 are actually the same equation.
\n" ); document.write( "Let's look at eq. 2 more closely,
\n" ); document.write( "2. $\"3x-4%28y-2%29=28-x\"$
\n" ); document.write( " $\"3x-4y%2B8=28-x\"$
\n" ); document.write( " $\"3x-4y%2B8=28-x\"$
\n" ); document.write( " $\"-4y=20-4x\"$
\n" ); document.write( " $\"y=%2820-4x%29%2F%28-4%29\"$
\n" ); document.write( " $\"y=-5%2Bx\"$
\n" ); document.write( " $\"y=x-5\"$
\n" ); document.write( "Since eq. 1 and eq. 2 are the same, this is a dependent system of equations.
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