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How do you solve simultaneous equations using the substitution method ?x=y  ...

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jessie01 | Student, Grade 11 | (Level 2) Honors

Posted March 17, 2010 at 1:46 PM via web

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How do you solve simultaneous equations using the substitution method ?

x=y   6x-2y=10        x=-y    3x-6y=36


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pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted March 17, 2010 at 1:53 PM (Answer #1)

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So these are two separate simultaneous equations, right?  And x actually equals y in the first one?

If so, in the first one, just substitute y for x.  Then you will have 6y - 2y = 10.  That becomes 4y = 10 and that becomes y = 2.5.

The other one is a little more complicated since x = -y, but it's the same process.  You substitute -y for x.  Then you will have

-3y - 6y = 36

That gets you

-9y = 36

And y = -4

Since x = -y, x = -(-4).  Two negatives make a positive and x = 4

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job518 | College Teacher | (Level 2) Adjunct Educator

Posted March 17, 2010 at 2:10 PM (Answer #2)

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I am assuming that we are talking about 2 different systems since x=y in the first and x=-y in the second.

For the first system where x = y, simply substitute x for y. Then 6x - 2y  becomes 6x -2x. So 6x -2x = 4x =10. Divide both sides by 4 and you have x = 2.5 => y = 2.5.

For the second system: 

Since x = -y, then replace x with -y. Then 3x - 6y becomes 3(-y) - 6y.  Now, we have -3y - 6y = -3y + -6y = -9y =36. Divide both sides by -9 and we have y= - 4 => -y = 4 => x = 4. 

If you need to solve each with x=y and x=-y, then you would follow the same steps for the other equation. In other words, use x = -y for substituting in 6x - 2y. Then you would have 6(-y) - 2y = -6y - 2y = -8y = 10. Divide both sides by -8 and get y = -1.25. Since x= -y, the x = 1.25.

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epollock | (Level 3) Valedictorian

Posted March 17, 2010 at 2:40 PM (Answer #3)

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Simultaneous equations are solved by substituting one variable for the other and setting the equation equal to 0, or if it has a constant. This is simply done by exchanging one for the other, for example, x=y, 6x-2y=10. You have to substitute y for x and the equation becomes:




The other equations for y, substituting x for y is the same process.





It is a very easy and straightforward process for you to solve similar equations using the same process.

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neela | High School Teacher | (Level 3) Valedictorian

Posted March 17, 2010 at 3:51 PM (Answer #4)

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There are two pairs  pair of equations, each pair having two variables x and y.

First pair:

x=y.....................(i) and


are simultaneous linear equations in two variables x and y.

Since x=y , substitute y = x in (ii) and we get: 6x-2x = 10. Or 4x = 10 . Therefore,  x = 10/4 = 2.5. Since y = x, y = 2.5

Second Pair:

x=-y ..................(1) and

3x-6y=36 ...........(2).

Though it is easy to substitute x= -y, we go different. From the second equation (dividing both sides by 3) we get x-2y = 12 . Or x = 12+2y. Substituting this x in terms of y in (1), we get:

12+2y = -y Or Subtracting 2y from both sides, we get:

12 = -3y Or y = 12/-3 = -4. So x =-y = -(-4) = 4.

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Wiggin42 | Student, Grade 11 | (Level 2) Valedictorian

Posted July 8, 2014 at 12:46 PM (Answer #5)

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The substitution method involves replacing the variable in one equation with another variable. For  example, in both cases we are told what x equals in terms of y. Replace every instance of x in the other equation with this y value. Then you will have only one equation in terms of y which you can solve for easily. Then plug this back into the other equation to solve for x.

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