Mathematics
Grade10
Easy

Question

Solve the system:
y = x + 3
5y = 5x + 15

  1. No solution
  2. (11, 8)
  3. (5, 15)
  4. Infinitely many solutions.

Hint:

we have given two equation, we have to solve the system. We have two equation which  is y = x  + 3 and 5y = 5x + 15 .Make two equation , if (a1/a2) = (b1/b2) = (c1/c2) then it is infinitely many solutions, if  (a1/a2) = (b1/b2) ≠ (c1/c2) and if (a1/a2) ≠(b1/b2) then it is unique solution.

The correct answer is: Infinitely many solutions.


    Here we have to find the system of equation.
    Firstly, we have given equation y = x + 3 and 5y = 5x + 15.
    So ,
    y = x + 3         --(1)
    5y = 5x + 15   --(2)
    We have a1 = 1 , b1 = 1 and c1 = 3
    And a2 = 5 , b2 = 5 and c2 = 15,
    Now,
    a1/a2 = 1/5 ,b1/b2 = 1/5 and c1/ c2 = 3/15 = 1/5
    Therefore, a1/a2 = b1/b2 = c1/c2
    Therefore , it solution having infinitely many solution.
    The correct answer is Infinitely many solution.
    Or, another way .
    y = x + 3 …(i)
    5y = 5x + 15 …(ii)
    Substituting y from (i) in (ii), we get
    5(x + 3) = 5x + 15
    5x + 15 = 5x + 15
    15 = 15
    The statement 15 = 15 is an identity, so the system of equations has infinitely many solutions.

    In this question, we have solve this question by system of equation we have , if (a1/a2) = (b1/b2) = (c1/c2) then it is infinitely many solutions, if  (a1/a2) = (b1/b2) ≠ (c1/c2) and if (a1/a2) ≠(b1/b2) then it is unique solution.

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