Mathematics
Grade10
Easy

Question

Solve the system:
y = 3x + 15
3x – y = -4

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

Hint:

In this question, we are given two system of equation , we have to find the value x and y. 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: No solution


    Here we have solve the system of equation and find x and y.
    Firstly , we are given, y = 3x + 15 and 3x – y = -4
    So we can write,
    y= 3x +15
    3x – y = -15   -------( 1)
    3x – y = -4     --------(2)
    Now , we have a1/a2
    a1/a2 = 3/3 =1
    and b1/b2 ,
    b1/b2 = -1/-1 = 1
    and c1/c2
    c1/c2 = (-15)/(-4)= 15/4
    so here,
    1 = 1 ≠ 15/4
    a1/a2 = b1/b2 ≠ c1/c2
    Therefore the system of equation of no solution.
    The correct answer is No solution.
    or, another way to solve.
    y = 3x + 15 …(i)
    3x – y = -4 …(ii)
    Substituting y from (i) in (ii), we get
    3x – (3x + 15) = -4
    15 = -4
    The statement 15 = –4  is false, so the system of equations has no solution.

    In this question, we have to find the system of 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.

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