document.write( "Question 174019: I'm not sure how to do this problem, it asks to solve by system of equations.
\n" ); document.write( "x+7y=8
\n" ); document.write( "x=6-7y
\n" ); document.write( "I think the equal signs being in different places has me confused. \n" ); document.write( "
Algebra.Com's Answer #128927 by gonzo(654)\"\" \"About 
You can put this solution on YOUR website!
you have to manipulate the equations until everything is in the same place.
\n" ); document.write( "you do this following the rules of algebra by:
\n" ); document.write( "-----
\n" ); document.write( "subtracting the same value from both sides of the equation.
\n" ); document.write( "or:
\n" ); document.write( "adding the same value from both sides of the equation.
\n" ); document.write( "or:
\n" ); document.write( "multiplying each side of the equation by the same value.
\n" ); document.write( "or:
\n" ); document.write( "dividing each side of the equation by the same value.
\n" ); document.write( "or:
\n" ); document.write( ".....
\n" ); document.write( "you can do more (raise each side to the same power, take each side to the same root) but this should be enough for what you need.
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\n" ); document.write( "your problem:
\n" ); document.write( "x + 7y = 8
\n" ); document.write( "and
\n" ); document.write( "x = 6 - 7y
\n" ); document.write( "-----
\n" ); document.write( "if you need to solve this as a system of equations then i believe you need to make both equations in the standard form.
\n" ); document.write( "-----
\n" ); document.write( "the first equation looks like it already is in the standard form:
\n" ); document.write( "that is
\n" ); document.write( "x + 7y = 8
\n" ); document.write( "-----
\n" ); document.write( "the second equation needs a little manipulating.
\n" ); document.write( "that equation starts out as:
\n" ); document.write( "x = 6 - 7y
\n" ); document.write( "first you add 7y to both sides of the equation.
\n" ); document.write( "x + 7y = 6 - 7y + 7y
\n" ); document.write( "once you combine like terms, that equation becomes:
\n" ); document.write( "x + 7y = 6
\n" ); document.write( "because the -7y and the 7y on the right hand side of the equation cancel out.
\n" ); document.write( "-----
\n" ); document.write( "you have just moved 7y from the right side of the equation to the left side of the equation using the laws of algebra.
\n" ); document.write( "-----
\n" ); document.write( "that equation is now also in standard form.
\n" ); document.write( "you have 2 equations:
\n" ); document.write( "x + 7y = 8
\n" ); document.write( "x + 7y = 6
\n" ); document.write( "-----
\n" ); document.write( "these equations look identical except for what's on the right side of the equation.
\n" ); document.write( "if you subtract the second equation from the first equation, you get:
\n" ); document.write( "0 = 2
\n" ); document.write( "since this is impossible, your equations cannot be solved simultaneously.
\n" ); document.write( "-----
\n" ); document.write( "to prove this, i will solve the equations by substitution.
\n" ); document.write( "if i get the same answer then i know for sure.
\n" ); document.write( "solving by substitution works as follows:
\n" ); document.write( "your original equations are:
\n" ); document.write( "x + 7y = 8
\n" ); document.write( "x = 6 - 7y
\n" ); document.write( "-----
\n" ); document.write( "since x = 6-7y, you substitute 6-7y for x in your first equation.
\n" ); document.write( "6 - 7y + 7y = 8
\n" ); document.write( "6 = 8
\n" ); document.write( "this is not possible therefore your equations do not have a solution.
\n" ); document.write( "-----
\n" ); document.write( "i came up with no solution both ways.
\n" ); document.write( "i believe that's your answer.\r
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