Mathematics
Grade10
Easy
Question
Solve the system:
y = -x + 10
x + y = 10
- 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 = x + 3 and 5y = 5x + 15 .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 = -x + 10 and x + y = 10.
So ,
y = -x + 10 --(1)
x + y = 10 --(2)
We have a1 = 1 , b1 = 1 and c1 = 10
And a2 = 1 , b2 = 1 and c2 = 10,
Now , a1/a2 = 1,
b1/b2 = 1
and c1/ c2 = 10/10 = 1
Therefore, a1/a2 = b1/b2 = c1/c2
Therefore , it solution having infinitely many solution.
The correct answer is Infinitely many solution.
Or, another way to solve
y = -x + 10 …(i)
x + y = 10 …(ii)
Substituting y from (i) in (ii), we get
x + (-x + 10) = 10
10 = 10
The statement 10 = 10 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.
