You can
put this solution on YOUR website!Hi, Hope I can help,
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solve the system:
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x+3y+5z=20
y-4z=(-16)
3x-2y+9z=36
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This is the way I usually solve these problems(pretty easy once you know how to do it) ( There is no fast way to solve these problems)
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First, solve for a letter in all the equations( since we already have a 2 system/variable equation for equation 2, we don't have to solve for any letter in equation 2)( Since
that means we will need to solve for "x" in our other equations)
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We will rewrite the 3 equations so it makes more sense( the second equation has no "x's" in the equation so it has "0x")
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x+3y+5z=20
0x + y - 4z =( -16)
3x-2y+9z=36
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We will switch the equations around
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x+3y+5z=20
3x-2y+9z=36
0x + y - 4z = (-16)
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We will solve "x" in our first two equations(can't solve "x" in our third equation, since it is 0x)
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First equation
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We will move "3y" over to the right side
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=
.
=
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We will move "5z" to the right side
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=
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=
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We will switch the letters around
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=
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This is our First Answer
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We will now solve "x" in our second equation
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We will move (-2y) to the right side
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=
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=
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We will move "9z" to the right side
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=
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=
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We will switch the letters around
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=
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We will now divide each side by "3"
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=
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=
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Our second answer =
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We can now solve to get a 2 system(variable) equation
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We will put our two answers together in an equation, since "x" = both of the answers, our answers equal each other
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First answer =
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Second answer =
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Our equation will equal
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=
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We will use cross multiplication to get rid of the fractions
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We will move (-9y) to the right side
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=
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We will move the (-15z) to the right side
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=
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=
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We will move the "36" to the left side
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=
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=
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We will rearrange,
=
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Our second 2 system/variable equation =
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We will put our two 2 system/variable equations side by side
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First equation =
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Second equation =
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We will now need to solve for a letter again( we will solve "y" since it is the easiest to solve)
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First equation
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We will move (-4z) to the right side
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=
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=
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=
( rearranging the numbers)
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Our first answer =
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Our second equation
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We will move "6z" to the right side
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=
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=
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Rearranging
=
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We will divide each side by "11"
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=
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=
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=
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Our second answer is
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We can now put both of our answers into an equation( since "y" equals both of our answers)
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Answer 1 =
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Answer 2 =
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We can make our equation, it equals
.
=
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We will cross multiply to get rid of the fractions
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It becomes,
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We will move (-6z) to the left side
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=
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=
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We will move (-176) to the right side
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=
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=
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We will divide each side by "50"
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=
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=
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=
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We found that "z" = 4, we can replace "z" with "4" in one of our 2 system/variable equations
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We will use the first equation
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=
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=
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We will move (-16) to the right
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=
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=
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We found that "y" = "0"
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We can now find "x", we need to replace "y" and "z" in one of the three original equations
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y = 0
z = 4
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x+3y+5z=20
y-4z=(-16)
3x-2y+9z=36
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We will use the first equation, since it will be the easiest( we can't use the second equation)
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=
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=
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=
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We will move the "20" over to the right side
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=
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We found that "x" = "0", we now have all 3 variables, "x","y", and "z"
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x = 0
y = 0
z = 4
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We can check by replacing the letters with numbers in our third equation
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=
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=
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=
( True)
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x = 0
y = 0
z = 4
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The solution set = (x,y,z), our solution set = (0,0,4)
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Hope I helped, Levi
