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.