document.write( "Question 117668: what are the steps when solving an equation using substitution \n" ); document.write( "

Algebra.Com's Answer #85976 by MathLover1(20850) $\"\"$ $\"About$

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Steps to solve a system of equations by the substitution method:
\n" ); document.write( "In general, if you solve a system of equations and the result is a true statement, such as $\"-+8+=+-8\"$ , the system has $\"+infinitely\"$ many $\"solutions\"$ ; if the result is a false statement, such as $\"-+5+=+7\"$ , the system has $\"no\"$ $\"+solution\"$ .
\n" ); document.write( "We will start with an example to show the steps in solving a system of equations by the substitution method:\r
\n" ); document.write( "\n" ); document.write( "Use substitution to solve the system of equations # $\"1\"$ -> $\"+x+%2B+y+=+1\"$ and # $\"2\"$ -> $\"2x+%2B+y+=+-+1\"$ .
\n" ); document.write( "Step 1:
\n" ); document.write( "Solve one of the equations for $\"+x\"$ or $\"y\"$ . Let it be: solve for $\"x\"$ from equation # $\"1.\"$ since the coefficient of $\"x\"$ is $\"1\"$ .
\n" ); document.write( " $\"x+%2B+y+=+1\"$
\n" ); document.write( " $\"x+=+1-+y+\"$
\n" ); document.write( "Step 2:
\n" ); document.write( " Substitute this value into the other equation. Use the # $\"2.\"$ equation.
\n" ); document.write( " $\"2x+%2B+y+=+-+1\"$ ЕЕЕЕЕЕЕЕ. use the # $\"2.\"$ equation.
\n" ); document.write( " $\"2%281+-+y%29+%2B+y+=+-1\"$ ЕЕЕЕЕ..substitute $\"1+%96+y\"$ for $\"x\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2+-+2y+%2B+y+=+-1\"$ ЕЕЕЕЕЕЕЕ.. distribute\r
\n" ); document.write( "\n" ); document.write( "Step 3:
\n" ); document.write( " Solve this equation.
\n" ); document.write( " $\"2+-+2y+%2B+y+=+-1\"$ ЕЕЕЕЕЕЕЕЕЕ.. solve for $\"y\"$
\n" ); document.write( " $\"-y+=+-3\"$ ЕЕЕЕЕЕЕЕ..divide both sides by $\"-1\"$
\n" ); document.write( " $\"y+=+3\"$
\n" ); document.write( "Step 4:
\n" ); document.write( "Find the value of the other variable using substitution into either equation.
\n" ); document.write( " $\"x+%2B+y+=+1\"$ ЕЕЕ. use the # $\"1.\"$ equation
\n" ); document.write( " $\"x+%2B+3+=+1\"$ ЕЕЕЕЕЕsubstitute $\"3\"$ for $\"y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x+=+-2\"$ ЕЕЕЕЕЕЕЕ.solution for $\"x\"$ \r
\n" ); document.write( "\n" ); document.write( "The solution to the $\"system\"$ is:
\n" ); document.write( " ( $\"x\"$ , $\"y\"$ ) = ( $\"-2\"$ , $\"3\"$ )
\n" ); document.write( "Check: Substitute $\"-2\"$ for $\"x\"$ and $\"3\"$ for $\"y\"$ in each of the original equations and check for true statements.
\n" ); document.write( " \n" ); document.write( "

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