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table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 7 x plus 3 y equals 8 end cell row cell 6 x minus 3 y equals 5 end cell end table
For the solution (x, y) to the system of equations above, what is the value of  x - y?

  1. negative 4 over 3
  2. 2 over 3
  3. 4 over 3
  4. 22 over 3

hintHint:

Linear equations in two variables can be solved by using the elimination method.
Explanation:
  • We have given a linear equation in two variables table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 7 x plus 3 y equals 8 end cell row cell 6 x minus 3 y equals 5 end cell end table.
  • We have to find the value of  (x - y) for the solution (x, y)
  • We will first solve the given equation using the elimination method, and then using the value of(x, y) , we can easily find the value of (x - y).

The correct answer is: 2 over 3


    Step 1 of 1:
    We have given an equation
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 7 x plus 3 y equals 8 end cell row cell 6 x minus 3 y equals 5 end cell end table
    Now, add both these equations, we will get 13 x equals 13.
    On further calculation,
    x equals 13 over 13
    x equals 1
    Now put this value of  in the first equation 7 x plus 3 y equals 8
    So, We will get
    7 left parenthesis 1 right parenthesis plus 3 y equals 8
    7 plus 3 y equals 8
    3 y equals 1
    y equals 1 third
    Step 2 of 2:
    Now, we will calculate the value of x - y.
    So,
    equals x minus y
    equals 1 minus 1 third
    equals 2 over 3
    Therefore, Option (b) is correct.

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