Mathematics
Grade-8
Easy

Question

Solve the following using the substitution method and find the value of x and y:
4x – 4y = 32
4x – 2y = 14

  1. 5, 3
  2. -5, -3
  3. -1, -9
  4. 1, 2

hintHint:

The substitution method is the algebraic method to solve simultaneous linear equations. , in this method, the value of one variable from one equation is substituted in the other equation. In this way, a pair of the linear equation gets transformed into one linear equation with only one variable, which can then easily be solved.

The correct answer is: -1, -9


    can then easily be solved.
    In this method, the elimination of the variable can be performed by substituting the value of another variable in an equation. Hence, this method is called the elimination by substitution method.
     4x – 4y = 32 and 4x – 2y = 14
    Given:
    4x – 4y = 32  …  (1)
    4x – 2y = 14 …(2)
    The equation (1) can be written as
    x- y = 8
    y = -8 + x … (3)
    Now, in equation (2) eliminate the variable y by substituting the value of y in terms of x from equation (3).
    Hence, equation (2) becomes
    4x - 2(-8 + x) = 14
    Now, apply the distributive property for the above equation,
    4x +16 -2x = 14
    2x = -2
    x = -1
    Hence, the value of x is -1.
    Now, substituting x= -1 in the equation (3), we get
    y = -8+ (-1)
    y = -9
    Therefore, the value of y is -9.
    Hence, the solution for the system of linear equations is:
    x = -1 and y= -9
    To check whether the obtained solution is correct or not, substitute the values of x and y in any of the given equations.
    Verification:
    Use Equation (2) to verify the solution
    4x – 2y = 14
    Now, substitute x= -1 and y= -9
    4(-1) - 2(-9) = 14
    -4 + '18= 14
    14 = 14
    Here, L.H.S = R.H.S
    Thus, the obtained solution is correct.

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