Question 174019
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.