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Question 170002: Solve by substitution or elimination method:
3x - 2y = 8
-12x + 8y = 32
Solve by substitution or elimination method:
7x - 5y = 14
-4x + y = 27
Solve by substitution or elimination method:
-4x + 3y = 5
12x - 9y = -15
Found 2 solutions by jim_thompson5910, Electrified_Levi:
Answer by jim_thompson5910(35256)   (Show Source):
Answer by Electrified_Levi(103) (Show Source):
You can put this solution on YOUR website! Hi, Hope I can help,
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Solve by substitution or elimination method:
.
3x - 2y = 8
-12x + 8y = 32
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Solve by substitution or elimination method:
.
7x - 5y = 14
-4x + y = 27
.
Solve by substitution or elimination method:
.
-4x + 3y = 5
12x - 9y = -15
.
First we will solve the first system with substitution
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3x - 2y = 8
-12x + 8y = 32
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First we need to solve for a variable in one of the two equations, doesn't matter which letter, or equation, we will solve for "y" in the first equation
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 , we will move (-2y) to the right side
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=  =  , now we need to move "8" to the left side
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=  =  , to find "y" we need to divide each side by "2"
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=  = 
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 , since "y" is equal to  , we can replace "y" in the other equation with , then just solve for "x"
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 =  , now just solve for "x"
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=  =  , now we will use the distribution method
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 = 
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Remember the + and - signs,  , adding the "x"'s
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=  =  ( False )
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This means ( when the x's or y's cancel out, and there is a false statement) that there are no solutions, these lines are parallel, there is no intersection, and therefore no solutions
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Here is the graph of this system
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Now we will solve the second system, by elimination
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7x - 5y = 14
-4x + y = 27
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Elimination is when you add the two equations together, and it gets rid of a variable, first we need to make sure the x's or y's in each equation are the same, or the negative of the other
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We can eliminate any variable ( either x or y )
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We will get rid of the y's
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We need to either get both y's to "5y" or "-5y" or we need to get them to "y" or "-y", we will change the second equation to "5y"
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 , to get "y" to change to "5y" we need to multiply each side by (5)
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=  = 
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We will need to use the distribution method
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=  = 
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Remember the signs,  , this is our new equation
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Now we will bring the firt equation to our second new equation
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We will now add the equations
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 = 
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 =  = 
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 = 
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It will become  =  , to find "x" we need to divide each side by 
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=  =  =  , we can now replace "x" with  , in one of the two original equations
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7x - 5y = 14
-4x + y = 27
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We will use the second equation
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=  =  = 
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Now we need to move  to the right side ( we will convert "27" into "13ths"
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 =  =  =  = 
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, we can check our answers by replacing "x" and "y" in both original equations
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First equation, =  =  =  =  =  =  ( True )
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Second equation, =  =  =  =  =  , ( True )
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Solution sets are in the form (x,y), our solution set is (  ,  )
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The graph of the system is
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The intersection is your answer
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Now we can do the last system
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-4x + 3y = 5
12x - 9y = -15
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We will use the elimination method of solving this problem
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Remember elimination is where you get rid of a variable
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We will multiply the first equation by "3" to get rid of the "y"
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 =  =  we will use distribution
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=  = 
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Remember signs,  , now we can add the new first equation to the second equation
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 =  =
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 =  = =
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 =  =
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It will become  =  (True)
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This means ( when both x and y cancel out, and there is a true statement) that this is the same line, both equation will be one line, there is an infinite number of solutions ( since the equations are equal to one line )( or the second line is put on the first line )
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Here is the graph of this system
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Your answers are
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First system of equations = " no solutions " ( since they are parallel lines )
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Second system of equations = ( , ) ( the lines intersect at point ( , )
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Third system of equations = " infinite solutions " ( since the two equations are the same line )
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Hope I helped, Levi
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