MathematicsSolve the following pair of linear equations by the cross-multiplication method and find the values of x and y respectively: x+2y=2 and x-3y=7   

Solve the following pair of linear equations by the cross-multiplication method and find the values of x and y respectively:


x+2y=2 and x-3y=7   


  1. A
    4,-1
  2. B
    -1,4
  3. C
    2,3
  4. D
    1,1 

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    Solution:

    Given that the pair of linear equations x+2y=2   and x3y=7  .
    To solve the equations a 1 x+by+ c 1 =0   and a 2 x+ b 2 y+ c 2 =0   by cross multiplication method, arrange the variables and the coefficients a 1 , a 2   and b 1 , b 2   and the constants c 1 , c 2   then x=b1c2-b2c1a1b2-a2b1  and y=a2c1-a1c2a1b2-a2b1 will be the required values of x and y.
    Here, a1=1,b1=2, c1=-2, a2=1,b2=-3, c2=-7.
    Putting the values to find the value of x,
    x=2×(-7)-(-3)×(-2)1×(-3)-1×2
    x=-14-6-3-2
    x=-20-5
    x=4
    Putting the values to find the value of y,
    y=(1)×(-2)-(1)×(-7)1×(-3)-1×2
    y=-2+7-3-2
    y=5-5
     y=-1
    Therefore, the value of x is 4 and the value of y is -1.
    Hence, option (1) is correct.
     
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