Mathematics
Grade10
Easy
Question
Solve the system:
y = -2x + 3
4x + 2y = 6
- 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 + 3 and 4x + 2y = 6.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 + 3 and 4x + 2y = 6.
So ,
y = -2x + 3 --(1)
4x + 2y = 6 --(2)
We have a1 = 2 , b1 = 1 and c1 = 3
And a2 = 4 , b2 = 2 and c2 = 6,
Now ,a1/a2 = 2/4 = 1/2 ,b1/b2 = 1/2 and c1/ c2 = 3/6 = 1/2
Therefore, a1/a2 = b1/b2 = c1/c2
Therefore , it solution having infinitely many solution.
The correct answer is Infinitely many solution.
Or, an another way to solve.
y = -2x + 3 …(i)
4x + 2y = 6 …(ii)
Substituting y from (i) in (ii), we get
4x + 2(-2x + 3) = 6
4x – 4x + 6 = 6
6 = 6
The statement 6 = 6 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.
