problem on substitution method

Topic: substitution method


When we used the Addition Method to solve a system of equations, we still had to do a substitution to solve for the remaining variable. With the substitution method, we solve one of the equations for one variable in terms of the other, and then substitute that into the other equation. This makes more sense with an example:

Question:

x+y=11,3x+y=5,Then solve for x.

Solution:

Let's use substitution method

 y = 11 - x

3x + y = 5

So,
    3x + 11 - x = 5

    2x + 11 = 5

    2x = 5 - 11

     2x = -6

      x = -3


Substitute it in the equation.

   y = 11 - x

   y = 11 - (-3)

   y = 11 + 3

   y = 14 is the answer

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Question on Substitution Method

Topic : Substitution Method

Question : Solve using substitution method.
x = 2y-9
x + 3y = 11

Solution :
x = 2y-9------(1)
x + 3y = 11----(2)
Putting the value of x in the second equation,
2y-9 + 3y = 11
2y+ 3y -9 = 11
5y -9 = 11 adding 11 on both sides
5y =20 dividing both sides with 5
y = 4 substituting in the first one
x = 2x4 – 9 =8- 9= -1 The solution is (-1, 4) or x =-1, y = 4.