Mathematics
Grade-8
Easy

Question

Solve the following using the substitution method and find the value of x and y:
-5x - 4y = 32
2y = -6

  1. 1, 4
  2. 4, 5
  3. -4, -3
  4. -5, -8

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: -4, -3


    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.
    -5x - 4y = 32 and 2y = -6
    Given:
    -5x - 4y = 32  …  (1)
    2y = -6 …(2)
    The equation (2) can be written as
    y = -3
    Hence, the value of y is -3.
    Now, substituting y= -3 in the equation (1), we get
    -5x - 4y = 32
    -5x - 4(-3) = 32
    -5x +12 = 32
    -5x = 20
    x = -4
    Therefore, the value of x is -4.
    Hence, the solution for the system of linear equations is:
    x = -4 and y= -3
    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 (1) to verify the solution
    -5x - 4y = 32
    Now, substitute x= -4 and y= -3
    -5(-4) - 4(-3) = 32
    20 + 12= 32
    32 = 32
    Here, L.H.S = R.H.S
    Thus, the obtained solution is correct.

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