Mathematics
Grade-8
Easy

Question

Solve the following pair of equations.
- 2 x + 3 y= 12 and 4 x + 3 y = - 6

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

hintHint:

The Linear Combination Method, aka The Addition Method , aka The Elimination Method. Add (or subtract) a multiple of one equation to (or from) the other equation, in such a way that either the x-terms or the y -terms cancel out. Then solve for x (or y, whichever's left) and substitute back to get the other coordinate.

The correct answer is: -3, 2


    There are different methods for solving simultaneous linear Equations:
    I. Elimination of a variable
    II. Substitution
    III. Cross-multiplication
    IV. Evaluation of proportional value of variables 
    Here, we will be using Elimination of a variable method.
    Here, we have 2 equations
    - 2x + 3y= 12  can also be written as 2x - 3y = -12                       (1)
    4x + 3 y = -6             (2)
    Multiplying 2 in equation(1), we get:
    2  (2x - 3y = -12) = 4x -6y = -24              (3)
    Subtracting equation 1 and 3 , we get :
    4x - 6y = -24
    -
    4x +3y = -6
    ___________
    = -9y = -18
    y= 2
    Substitute the value of y in equation (2), we get:
    4x +3(2) = -6
    x= -3
    Thus, (x, y) = (-3, 2)

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