Mathematics
Grade10
Easy
Question
Solve the system:
y = 2x + 8
3y = 6x + 24
- No solution
- (11, 8)
- (5, 15)
- Infinitely many solutions.
Hint:
we have given two equation, we have to solve the system. We have two equation which is y = 2x + 8 and 3y = 6x + 24 .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 = 2x + 8 and 3y = 6x + 24.
So ,
y = 2x + 8 --(1)
3y = 6x + 24 --(2)
We have a1 = 2 , b1 = 1 and c1 = 8
And a2 = 6 , b2 = 3 and c2 = 24,
Now , a1/a2 = 1/3 ,
b1/b2 = 1/3
and c1/ c2 = 8/24 = 1/3
therefore, a1/a2 = b1/b2 = c1/c2
Therefore , it solution having infinitely many solution.
The correct answer is Infinitely many solution.
Or,
y = 2x + 8 …(i)
3y = 6x + 24 …(ii)
Substituting y from (i) in (ii), we get
3(2x + 8) = 6x + 24
6x + 24 = 6x + 24
24 = 24
The statement 24 = 24 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.
