Mathematics
Grade10
Easy
Question
Solve the system:
y = 2x + 8
3y = 6x + 30
- No solution
- (11, 8)
- (5, 15)
- 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 + 8 and 3y = 6x + 30
So we can write,
2x – y = -8 -------( 1)
6x – 3y = -30 -------(2)
Now , we have a1/a2
a1/a2 = 2/6 =1/3
and b1/b2 ,
b1/b2 = -1/-3 = 1/3
and c1/c2
c1/c2 = -8/-30= 4/15
so here,
1/3 = 1/3 ≠ 4/15
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 question..
y = 2x + 8 …(i)
3y = 6x + 30 …(ii)
Substituting y from (i) in (ii), we get
3(2x + 8) = 6x + 30
6x + 25 = 6x + 30
25 = 30
The statement 25 = 30 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.
