Mathematics
Grade-8
Easy

Question

-5x – 2y = 9
-2x + 3y = 15

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

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, 3


    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
    -5x – 2y = 9   can also be written as 5x + 2y = -9                       (1)
    -2x + 3y = 15  can also be written as 2x - 3y = -15             (2)
    Multiplying 2 in equation(1)  and 5 in equation (2), we get:
    cross times (5x + 2y = -9) = 10x +4y = -18              (3)
    cross times (2x - 3y = -15) = 10x -15y = -75            (4)
    Subtracting equation 3 and 4 , we get :
    10x + 4y = -18
    -
    10x –15y = -75
    ___________
    = 19y = 57
    y= 3
    Substitute the value of y in equation (2), we get:
    2x -3(3) = -15
    x= -3
    Thus, (x, y) = (-3, 3)

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