Mathematics
Grade10
Easy

Question

Solve the system:
y = -2x + 20
2x + y = 10

  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 = -2x + 20 and 2x + y = 10
    So we can write,
    y = -2x + 20 -------( 1)
    2x + y = 10 --------(2)
    Now , we have a1/a2
    a1/a2 = 2/2 =1
    and b1/b2 ,
    b1/b2 = 1/1 = 1
    and c1/c2
    c1/c2 = 20/10= 2
    so here,
    1 = 1 ≠ 2
    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 the question,
    y = -2x + 20 …(i)
    2x + y = 10 …(ii)
    Substituting y from (i) in (ii), we get
    2x + (-2x + 20) = 10
    20 = 10
    The statement 20 = 10 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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