SOLUTION: I'm not sure how to do this problem, it asks to solve by system of equations. x+7y=8 x=6-7y I think the equal signs being in different places has me confused.

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Question 174019: I'm not sure how to do this problem, it asks to solve by system of equations.
x+7y=8
x=6-7y
I think the equal signs being in different places has me confused.
Found 2 solutions by solver91311, gonzo:
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!
Your system is set up to be solved using the substitution method. The second equation gives you an expression that is equal to , so you can just substitute that expression in place of in the first equation, leaving you with an equation in a single variable, , that can be solved by ordinary methods.

Remember, if in the process of solving a system you obtain an absurd result, something like , that means that you have an inconsistent system. In other words, the solution set of the system is the empty set. Graphically speaking, the equations represent two straight lines that are parallel and so never intersect.

Answer by gonzo(654) (Show Source):
You can put this solution on YOUR website!
you have to manipulate the equations until everything is in the same place.
you do this following the rules of algebra by:
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subtracting the same value from both sides of the equation.
or:
adding the same value from both sides of the equation.
or:
multiplying each side of the equation by the same value.
or:
dividing each side of the equation by the same value.
or:
.....
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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your problem:
x + 7y = 8
and
x = 6 - 7y
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if you need to solve this as a system of equations then i believe you need to make both equations in the standard form.
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the first equation looks like it already is in the standard form:
that is
x + 7y = 8
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the second equation needs a little manipulating.
that equation starts out as:
x = 6 - 7y
first you add 7y to both sides of the equation.
x + 7y = 6 - 7y + 7y
once you combine like terms, that equation becomes:
x + 7y = 6
because the -7y and the 7y on the right hand side of the equation cancel out.
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you have just moved 7y from the right side of the equation to the left side of the equation using the laws of algebra.
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that equation is now also in standard form.
you have 2 equations:
x + 7y = 8
x + 7y = 6
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these equations look identical except for what's on the right side of the equation.
if you subtract the second equation from the first equation, you get:
0 = 2
since this is impossible, your equations cannot be solved simultaneously.
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to prove this, i will solve the equations by substitution.
if i get the same answer then i know for sure.
solving by substitution works as follows:
your original equations are:
x + 7y = 8
x = 6 - 7y
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since x = 6-7y, you substitute 6-7y for x in your first equation.
6 - 7y + 7y = 8
6 = 8
this is not possible therefore your equations do not have a solution.
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i came up with no solution both ways.
i believe that's your answer.